Recent zbMATH articles in MSC 83Chttps://zbmath.org/atom/cc/83C2023-05-31T16:32:50.898670ZWerkzeugElementary integral series for Heun functions: application to black-hole perturbation theoryhttps://zbmath.org/1508.330112023-05-31T16:32:50.898670Z"Giscard, P.-L."https://zbmath.org/authors/?q=ai:giscard.pierre-louis"Tamar, A."https://zbmath.org/authors/?q=ai:tamar.avivSummary: Heun differential equations are the most general second order Fuchsian equations with four regular singularities. An explicit integral series representation of Heun functions involving only elementary integrands has hitherto been unknown and noted as an important open problem in a recent review. We provide such representations of the solutions of all equations of the Heun class: general, confluent, bi-confluent, doubly confluent, and triconfluent. All the series are illustrated with concrete examples of use, and Python implementations are available for download. We demonstrate the utility of the integral series by providing the first representation of the solution to the Teukolsky radial equation governing the metric perturbations of rotating black holes that is convergent everywhere from the black hole horizon up to spatial infinity.
{\copyright 2022 American Institute of Physics}The Noether theorems in contexthttps://zbmath.org/1508.370862023-05-31T16:32:50.898670Z"Kosmann-Schwarzbach, Yvette"https://zbmath.org/authors/?q=ai:kosmann-schwarzbach.yvetteSummary: This chapter sketches the contents of Noether's 1918 article, `Invariante Variationsprobleme', as it may be seen against the background of the work of her predecessors and in the context of the debate on the conservation of energy that had arisen in the general theory of relativity.
For the entire collection see [Zbl 1497.37002].Negatively curved Einstein metrics on ramified covers of closed four-dimensional hyperbolic manifoldshttps://zbmath.org/1508.530572023-05-31T16:32:50.898670Z"Premoselli, Bruno"https://zbmath.org/authors/?q=ai:premoselli.brunoSummary: This paper is a shortened version of the recent article \textit{Examples of compact Einstein four-manifolds with negative curvature} [J. Am. Math. Soc. 33, No. 4, 991--1038 (2020; Zbl 1467.53055)] written in collaboration with \textit{J. Fine} (ULB). Its content was presented by the author at the \textit{Séminaire de Théorie Spectrale et Géométrie} in Grenoble in December 2017. In [loc. cit.], new examples of compact, negatively curved Einstein manifolds of dimension 4 have been
obtained. These are seemingly the first such examples which are not locally homogeneous. The Einstein metrics we construct are carried by a sequence of 4-manifolds \((X_k)\), previously considered by \textit{M. Gromov} and \textit{W. P. Thurston} [Invent. Math. 89, 1--12 (1987; Zbl 0646.53037)], and obtained as ramified coverings of closed hyperbolic 4-manifolds. Our proof relies on a deformation procedure. We first find an approximate Einstein metric on \(X_k\) by interpolating
between a model Einstein metric near the branch locus and the pull-back of the hyperbolic metric from the base hyperbolic manifolds. We then perturb to a genuine solution to Einstein's equations, by a parameter dependent version of the inverse function theorem.
For the entire collection see [Zbl 1499.35006].Interval topology in contact geometryhttps://zbmath.org/1508.530892023-05-31T16:32:50.898670Z"Chernov, Vladimir"https://zbmath.org/authors/?q=ai:chernov.vladimir-m|chernov.vladimir-v|chernov.vladimir-g"Nemirovski, Stefan"https://zbmath.org/authors/?q=ai:nemirovskij.stefan-yuSummary: A topology is introduced on spaces of Legendrian submanifolds and groups of contactomorphisms. The definition is motivated by the Alexandrov topology in Lorentz geometry.Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchieshttps://zbmath.org/1508.531002023-05-31T16:32:50.898670Z"Bubuianu, Iuliana"https://zbmath.org/authors/?q=ai:bubuianu.iuliana"Vacaru, Sergiu I."https://zbmath.org/authors/?q=ai:vacaru.sergiu-ion"Veliev, Elşen Veli"https://zbmath.org/authors/?q=ai:veliev.elsen-veliSummary: We investigate classical and quantum geometric information flow theories (GIFs and QGIFs) when the geometric flow evolution and field equations for nonholonomic Einstein systems, NES, are derived from Perelman-Lyapunov-type entropic-type functionals. The term NES encodes models when the fundamental physical equations are subjected to nonholonomic (equivalently, nonintegrable, anholonomic) constraints. There are used canonical geometric variables that allow a general decoupling and integration of systems of nonlinear partial differential equations describing GIFs and QGIFs and Ricci soliton-type configurations. Our approach is different from the constructions elaborated for special classes of solutions characterized by area-hypersurface entropy, related holographic, and dual gauge-gravity models involving generalizations of the Bekenstein-Hawking entropy. We formulate the theory of QGIFs which in certain quasi-classical limits encodes GIFs and models with flow evolution of NES. There are computed, respectively, the von Neumann, relative and conditional entropy; mutual information, entanglement, and Rényi entropy. We construct explicit examples of generic off-diagonal exact and parametric solutions describing stationary solitonic gravitational hierarchies and deformations of black hole configurations. Finally, we show how Perelman's thermodynamic values and extensions to QGIF models can be computed for various new classes of exact solutions which cannot be described following the Bekenstein-Hawking approach.Classical and quantum geometric information flows and entanglement of relativistic mechanical systemshttps://zbmath.org/1508.531012023-05-31T16:32:50.898670Z"Vacaru, Sergiu I."https://zbmath.org/authors/?q=ai:vacaru.sergiu-ion"Bubuianu, Laurenţiu"https://zbmath.org/authors/?q=ai:bubuianu.laurentiuSummary: This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange-Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with methods of computation are developed in general covariant form for curved phase spaces modelled as cotangent Lorentz bundles. The constructions are based on ideas relating the Grigori Perelman's entropy for geometric flows and associated statistical thermodynamic systems to the quantum von Neumann entropy, classical and quantum relative and conditional entropy, mutual information, etc. We formulate the concept of the entanglement entropy of quantum geometric information flows and study properties and inequalities for quantum, thermodynamic and geometric entropies characterizing such systems.Knotted 4-regular graphs: polynomial invariants and the Pachner moveshttps://zbmath.org/1508.570302023-05-31T16:32:50.898670Z"Cartin, Daniel"https://zbmath.org/authors/?q=ai:cartin.danielSummary: In loop quantum gravity, states of quantum geometry are represented by classes of knotted graphs, equivalent under diffeomorphisms. Thus, it is worthwhile to enumerate and distinguish these classes. This paper looks at the case of 4-regular graphs, which have an interpretation as objects dual to triangulations of three-dimensional manifolds. Two different polynomial invariants are developed to characterize these graphs -- one inspired by the Kauffman bracket relations and the other based on quandles. How the latter invariant changes under the Pachner moves acting on the graphs is then studied.
{\copyright 2022 American Institute of Physics}High-performance implementation of a Runge-Kutta finite-difference scheme for the Higgs boson equation in the de Sitter spacetimehttps://zbmath.org/1508.650842023-05-31T16:32:50.898670Z"Balogh, Andras"https://zbmath.org/authors/?q=ai:balogh.andras"Banda, Jacob"https://zbmath.org/authors/?q=ai:banda.jacob"Yagdjian, Karen"https://zbmath.org/authors/?q=ai:yagdjian.karenSummary: High performance computations are presented for the Higgs boson equation in the de Sitter spacetime using explicit fourth order Runge-Kutta scheme on the temporal discretization and fourth order finite difference discretization in space. In addition to the full, \((3+1)\)-dimensional equation we also examine the \((1+1)\)-dimensional radial solutions. The numerical code for the \((3+1)\)-dimensional equation is programmed in CUDA Fortran and is performed on NVIDIA Tesla K40c GPU Accelerators. The radial form of the equation is simulated in MATLAB. The numerical results demonstrate the existing theoretical result that under certain conditions bubbles form in the scalar field. We also demonstrate the known blow-up phenomena for the solutions of the related semilinear Klein-Gordon equation with imaginary mass. Our numerical studies suggest several previously not known properties of the solution for the Higgs boson equation in the de Sitter spacetime for which theoretical proofs do not exist yet: 1. smooth solution exists for all time if the initial conditions are compactly supported and smooth; 2. under some conditions no bubbles form; 3. solutions converge to step functions related to unforced, damped Duffing equations.Dynamics of three bodies located on a straight line for a finite speed of gravityhttps://zbmath.org/1508.700132023-05-31T16:32:50.898670Z"Slyusarchuk, Vu. Y."https://zbmath.org/authors/?q=ai:slyusarchuk.vu-ySummary: We study the dynamics of three bodies located on a straight line for a given finite speed of gravity in the case where the masses of external bodies and their distances to the central body are identical. It is shown that the motion of these bodies is unstable and the escape velocity is higher than the corresponding velocity in the classical celestial mechanics.Potentials vs geometry, revisitedhttps://zbmath.org/1508.780042023-05-31T16:32:50.898670Z"Curtright, T."https://zbmath.org/authors/?q=ai:curtright.thomas-l"Subedi, S."https://zbmath.org/authors/?q=ai:subedi.subhash|subedi.sanjeena|subedi.sauravSummary: We revisit an old subject to discuss relationships between the dynamics for particles subjected to potentials and the dynamics for particles moving freely on background geometries, in the context of non-relativistic quantum mechanics. In particular, we illustrate how selected geometries can be used to regularize singular potentials. We also compute scattering amplitudes for quanta incident on a static non-relativistic wormhole.
{\copyright 2022 American Institute of Physics}The geometry of quantum potential. Entropic information of the vacuumhttps://zbmath.org/1508.810072023-05-31T16:32:50.898670Z"Fiscaletti, Davide"https://zbmath.org/authors/?q=ai:fiscaletti.davideThis book consists of 4 chapters in which the author argues for why Bohm's approach with respect to quantum physics is more preferable than the other approaches. This is explained to some extent in the introduction and elaborated during the book. In chapter 1, the geometry of the quantum potential in different contexts is discussed. In this chapter the author explains that if one wishes to develop a coherent geometrodynamic picture of the quantum world should accept that the quantum phenomena can not be explained as events occurring in space-time by standard interpretation of quantum mechanic. Thus we have to abandon the dogma of formulation of physics in terms of motion in space-time. To illustrate this, the author agrees that the probabilistic interpretation of the wavefunction developed by physicists of Copenhagen and Gottingen schools, is in agreement with the experimental facts of the microscopic world. But this has nothing against the possibility that wavefunction may have other hidden properties. The author mentions that Heisenberg observed that the standard interpretation is a-causal and this means that the atomic processes can not be integrated into a space-time picture. The author stipulates that if one does not want to reduce physics to a kind of algorithm which is efficiently fits in to correlate the statistical results of experiments, then one should be ready to develop a real geometrodynamic picture of the quantum world based on causal understanding of the microscopic world as a connected series of individual processes. For doing this one should search for possible further significances of the wavefunction and introduce other elements in addition to the wavefunction. Here the author explains that Bohm's version of quantum mechanics suggests a formulation of quantum mechanics for which probability is considered as a supplementary condition on a causal theory of the motion of individual events. This approach is originally proposed by Louis de Broglie in 1927 at the Solvay Conference. Considering the non-relativistic problem, de Brolgie proposed that the wavefunction of each one-body physical system is associated with a set of identical particles with different position which are distributed in space according to the usual quantum formula given by \(\mid \psi(\vec{x})\mid^2\). In his analysis, he considered a dual role for the wavefunction, that is, a probable position of the particle and influence of the position by exerting a force on the orbit. In 1952 David Bohm rediscovered this approach and extended de Broglie's approach. This is the reason why in the literature this approach is called de Broglie-Bohm pilot wave theory. Thus , based on this approach, the author in Chapter 1 discusses the geometrodynamic features of the quantum potential and its geometry in non relativistic de Brolgie-Bohm theory, in relativistic quantum mechanics, in relativistic quantum field theory, in quantum gravity and cosmology. The author also discusses the link between Bohm's quantum potential and Weyl geometries. Analysing the features of the quantum potential, he discusses Grössing's thermodynamic approach. in Subsection 1.3.2, he brings Santamato's contribution to the geometric interpretation of quantum mechanics. Santamato developed the de Broglie-Bohm formulation of quantum mechanics by relating the mysterious quantum potential to the fundamental geometric properties in the context of Weyl's geometry. In Section 1.4 he sets forth the subject of quantum potential in the relativistic domain in which in subsection 1.4.1 applies the quantum potential in Bohm's approach to Klein-Gordan relativistic quantum mechanics. Subsection 1.4.2 is dedicated to explain a de Broglie-Bohm like model for the Dirac equation which concerns the description of the behaviour of spin \(\frac{1}{2}\) particles in an relativistic regime. Section 1.5 concerns the quantum potential in relativistic quantum filed theory. The author tries to construct not only a Bohmian picture of the relativistic bosonic quantum field theory but also the fermionic quantum field theory. Section 1.6 is dedicated to the quantum potential in Bohmian quantum gravity. In section 1.7 the author gives an account of the quantum potential in Bohmian quantum cosmology since he believes that the Copenhagen interpretation can not be applied consistently. He points out that the fundamental element of de Broglie-Bohm interpretation, i.e., quantum potential has the merit to build a geometrodynamic picture of the behaviour of the universe as a whole. Chapter 2 is dedicated to the interpretation of Bohm's quantum potential in terms of a more fundamental entity called quantum entropy. The author extends this approach from non-relativistic domain to the relativistic one. He continues to apply this approach to Klein-Gordan relativistic quantum mechanics, to Dirac relativistic quantum mechanics, to relativistic quantum field theory, to quantum gravity and cosmology. The author in Chapter 3, analyses a recent development of the geometrodynamic approach of Bohm's quantum potential which is represented by a symmetrized quantum potential. This implies the existence of a three-dimensional timeless background as fundamental arena of quantum processes. The author presents an account of the extension of this approach to the relativistic curved space-time, the relativistic quantum field theory and the quantum cosmology. In Chapter 4, the author offers some consideration concerning the link between the quantum potential and the quantum vacuum intended as the fundamental arena of physical processes.
Reviewer: Saeid Jafari (Slagelse)On complementarity. A universal organizing principlehttps://zbmath.org/1508.810212023-05-31T16:32:50.898670Z"Avrin, Jack"https://zbmath.org/authors/?q=ai:avrin.jack-sPublisher's description: It is not uncommon for the Principle of Complementarity to be invoked in either Science or Philosophy, viz. the ancient oriental philosophy of Yin and Yang whose symbolic representation is portrayed on the cover of the book. Or Niels Bohr's use of it as the basis for the so-called Copenhagen interpretation of Quantum Mechanics. This book arose as an outgrowth of the author's previous book entitled ``Knots, Braids and Moebius Strips,'' published by World Scientific in 2015, wherein the Principle itself was discovered to be expressible as a simple $2\times 2$ matrix that summarizes the algebraic essence of both the well-known Microbiology of DNA and the author's version of the elementary particles of physics. At that point, the possibility of an even wider utilization of that expression of Complementarity arose.
The current book, features Complementarity, in which the matrix algebra is extended to characterize not only DNA itself but the well-known process of its replication, a most gratifying outcome. The book then goes on to explore Complementarity, with and without its matrix expression, as it occurs, not only in much of physics but in its extension to cosmology as well.
Contents:
Preliminaries: Introduction: Complementarity as a Principle, Deoxyribonucleic Acid, The Molecular Ladder to Life on Earth, Alternative Model Taxonomy, The AM/DNA Comparison, The Signature of Complementarity; Replication Unleashed. A (Particular) Connection to Chemistry.
Some Basic Physics: Dynamics, Thermodynamics, Energy-wise Comparison of Two Exercises, Maxwell's Equations and the Electromagnetic Field, Spacetime and The Ethereal Road to Relativity, Noether's Theorem and Gauge Theory.
General Relativity and the Geometry of Spacetime: General Relativity, Differential Geometry and The ``Action Enigma''; an Application, An Authoritative Perspective, And an Inference Thereof, An ``Indigenous Parallel'' to the Higgs, Undulation (or Undulatority). Another look at Our ``Indigenous Higgs Model''.
Quantum Mechanics and the Significance of Scale: Introducing Max Planck and the Quantum, Quantum Mechanics, Phase 1, Phase 2; Through the Looking Glass!, Quantum Mechanics, Radar and the Significance of Scale, The Fourier Transform and the Convolution Theorem, Nonlocality, Entanglement, and complementarity, Spin, Spinors, and the Pauli Connection, PAM Dirac, Mixmaster Extraordinaire.
Statistical Mechanics. Some Additional Alternative Model Topics: ``Deuteronomy'' and Isospin Invariance, Cosmological Complementarity, Gurule Loops
Summary and Conclusions: Recapitulation. Linking Complementarity and The Meaning of ``Is''Entropic uncertainty in the background of expanding de Sitter space-timehttps://zbmath.org/1508.811342023-05-31T16:32:50.898670Z"Huang, Zhiming"https://zbmath.org/authors/?q=ai:huang.zhimingSummary: We study the dynamics of quantum-memory-assisted entropic uncertainty for a hybrid qutrit-qubit system interacting with fluctuating quantum scalar field in the background of expanding de Sitter space. We firstly derive the master equation that the system evolution obeys. As evolution time goes by, for different initial states, entropic uncertainty develops to different fixed values for different parameter values, whereas entanglement always decays to zero, and there exist monotonous relations between entropic uncertainty, entanglement and various parameters for a fixed initial state, but mixedness behaves differently with entropic uncertainty and entanglement. Further it is found that the entropic uncertainty closely associated with the entanglement and mixedness. In addition, it is shown that the entropic uncertainty can be manipulated effectively via the weak measurement reversal. Our study would give some useful insights about the behavior characteristics of high-dimensional quantum system in expanding de Sitter space-time and may be useful to the tasks of quantum information processing of curved space-time since the uncertainty principle plays vital role in quantum information science and technology.Darwinian standard model of physics obtains general relativityhttps://zbmath.org/1508.814952023-05-31T16:32:50.898670Z"Lori, Nicolas"https://zbmath.org/authors/?q=ai:lori.nicolas-fSummary: A Darwinian perspective of the standard model of physics (SMP) quantum fields (QFs) is proposed, called the physics-cell (PC) approach. Because Darwinian evolution is not deterministic, the PC approach allows for the violation of the charge-parity-time symmetry. In the PC approach, the SMP laws are contained in the PCs which receive and emit QFs through the PCs' outer surface which is necessarily constrained by Bekenstein's surface-information limit. The establishment of gauge invariance-compatible communication protocol-agreements between the PCs obtains an average correlation of QFs that is equivalent to an asymmetric metric tensor with the symmetric component being equivalent to general relativity and the anti-symmetric component being very small but still large enough to allow for enough ex-nihilo mass-creation to explain dark matter. Based on experimental data, the PC minimum-size is \(1.5\cdot10^{-31}\) m which is similar to the scale at which the grand unified theory force convergence occurs. Plus, the cosmological constant energy density is equal to the energy density of the discreteness-correction QF alterations that constitute the dark energy and are caused by the finiteness of the PC time-step which equals \(5.0\cdot10^{-40}\) s, hence obtaining a PC maximum information processing rate of \(6.6\cdot10^{47}\) qubit/s. Moreover, the PC approach obtains that the minimum mass for black holes is \(2.1\cdot10^9\) larger than the maximum mass for which the no-hiding theorem can apply and that the maximum capacity for quantum computers is about \(29.0\cdot10^{12}\) qubit.Geometric approaches to quantum field theoryhttps://zbmath.org/1508.819322023-05-31T16:32:50.898670Z"Finn, Kieran"https://zbmath.org/authors/?q=ai:finn.kieranPublisher's description: The ancient Greeks believed that everything in the Universe should be describable in terms of geometry. This thesis takes several steps towards realising this goal by introducing geometric descriptions of systems such as quantum gravity, fermionic particles and the origins of the Universe itself.
The author extends the applicability of previous work by Vilkovisky, DeWitt and others to include theories with spin \(\frac{1}{2}\) and spin 2 degrees of freedom. In addition, he introduces a geometric description of the potential term in a quantum field theory through a process known as the Eisenhart lift. Finally, the methods are applied to the theory of inflation, where they show how geometry can help answer a long-standing question about the initial conditions of the Universe.
This publication is aimed at graduate and advanced undergraduate students and provides a pedagogical introduction to the exciting topic of field space covariance and the complete geometrization of quantum field theory.Fundamental scale invariancehttps://zbmath.org/1508.819362023-05-31T16:32:50.898670Z"Wetterich, C."https://zbmath.org/authors/?q=ai:wetterich.christofSummary: We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in terms of scale invariant fields. They correspond to exact scaling solutions of functional renormalization flow equations. Such theories are highly predictive since all relevant parameters for deviations from the exact scaling solution vanish. Realistic particle physics and quantum gravity are compatible with this setting. The non-linear restrictions for scaling solutions can explain properties as an asymptotically vanishing cosmological constant or dynamical dark energy that would seem to need fine tuning of parameters from a perturbative viewpoint. As an example we discuss a pregeometry based on a diffeomorphism invariant Yang-Mills theory. It is a candidate for an ultraviolet completion of quantum gravity with a well behaved graviton propagator at short distances.Infrared problem in perturbative quantum field theoryhttps://zbmath.org/1508.819392023-05-31T16:32:50.898670Z"Duch, Paweł"https://zbmath.org/authors/?q=ai:duch.pawelThe article is of undoubtible interest. It is based on few classic works which led to construction of the modern quantum electrodynamics. These are the works [\textit{L. Landau} and \textit{I. Pomeranchuk}, Dokl. Akad. Nauk SSSR 102, 489--492 (1955; Zbl 0067.21602)] and [\textit{N. N. Bogolyubov} and \textit{D. V. Shirkov}, Introduction to the theory of quantized fields. New York and London: Interscience Publishers (1959; Zbl 0088.21701)] which are most representative for quantum field theory, as well the article [\textit{S. W. Hawking} et al, ``Soft hair on black holes'', Phys. Rev. Lett. 116, No. 23, Article ID 231301, 9 p. (2016; \url{doi:10.1103/PhysRevLett.116.231301})] which is representative for Hawking's approach to quantum gravity including Black Holes.
The author is proposing a mathematically rigorous construction of the scattering matrix and the interacting fields in models of relativistic perturbative quantum field theory with massless field and long-range interactions. As a motivation for this new approach the author is invoquing the infrared problem arising in the standard definition of the scattering matrix.
The author's modified scattering matrix is based on the adiabatic limit which is expected to exist in arbitrary order of perturbation theory.
The author is concluding that the electrons and positrons are always surrounded by an irremovable cloud of photons, which agree with the conclussion of the article by L. D. Landau and I. Pomeranchuk cited above. The physical energy-momentum operators do not coincide wuith the standard ones and their joint spectrum does not contain the mass hyperboloid.
Reviewer: Alex B. Gaina (Chişinău)Optimal estimation of parameters for scalar field in an expanding spacetime exhibiting Lorentz invariance violationhttps://zbmath.org/1508.819422023-05-31T16:32:50.898670Z"Liu, Xiaobao"https://zbmath.org/authors/?q=ai:liu.xiaobao"Jing, Jiliang"https://zbmath.org/authors/?q=ai:jing.jiliang"Wang, Jieci"https://zbmath.org/authors/?q=ai:wang.jieci"Tian, Zehua"https://zbmath.org/authors/?q=ai:tian.zehuaSummary: We address the optimal estimation of quantum parameters, in the framework of local quantum estimation theory, for a massive scalar quantum field in the expanding Robertson-Walker universe exhibiting Lorentz invariance violation (LIV). We find that, in the estimation of cosmological parameters, the ultimate bounds to the precision of the Lorentz-invariant massive scalar field can be improved due to the effects of LIV under some appropriate conditions. We also show that, in the Lorentz-invariant massive scalar field and massless scalar field due to LIV backgrounds, the optimal precision can be achieved by choosing the particles with some suitable LIV, cosmological and field parameters. Moreover, in the estimation of LIV parameter during the spacetime expansion, we prove that the appropriate momentum mode of field particles and larger cosmological parameters can provide us a better precision.N-partite coherence of bosonic fields in the background of a Schwarzschild black holehttps://zbmath.org/1508.819432023-05-31T16:32:50.898670Z"Wu, Shu-Min"https://zbmath.org/authors/?q=ai:wu.shu-min"Li, Wen-Mei"https://zbmath.org/authors/?q=ai:li.wen-mei"Zeng, Hao-Sheng"https://zbmath.org/authors/?q=ai:zeng.haosheng"Huang, Xiao-Li"https://zbmath.org/authors/?q=ai:huang.xiaoliSummary: We study N-partite coherence of GHZ and W states for the free bosonic fields when \(n\) observers hover near the event horizon of the Schwarzschild black hole. It is shown that, with the increase of \(n\), the coherence of GHZ state decreases monotonously and occurs the phenomenon of irreversible decoherence, while the coherence of W state can increase monotonously, because the coherence of W state is equal to the sum of all bipartite coherence in the Schwarzschild black hole. For the first time, we find that the bosonic coherence is larger than the fermionic coherence in Schwarzschild spacetime, while the fermionic entanglement is larger than the bosonic entanglement in a relativistic setting. This suggests that, for different types of particles, we should use suitable quantum resources to deal with relativistic quantum information tasks.Multipartite quantum coherence and monogamy for Dirac fields subject to Hawking radiationhttps://zbmath.org/1508.819442023-05-31T16:32:50.898670Z"Wu, Shu-Min"https://zbmath.org/authors/?q=ai:wu.shu-min"Zeng, Hao-Sheng"https://zbmath.org/authors/?q=ai:zeng.haoshengSummary: We study the quantum coherence of Greenberger-Horne-Zeilinger-like states of multi-mode Dirac fields in the background of a Schwarzschild black hole. We find that the evolutions of both \(l_1\)-norm of coherence and relative entropy of coherence are similar, though the two measures are not completely compatible. The accessible coherence always degrades monotonically by the Hawking effect, and the inaccessible coherence increases from zero monotonically or non-monotonically, depending on the ratio of the inaccessible to the accessible number of modes. Both the accessible and inaccessible coherences have the phenomenon of freeze. The monogamies for the \(l_1\)-norm of coherence between the accessible and inaccessible modes are established.Radiative generation of realistic neutrino mixing with \(A4\)https://zbmath.org/1508.819682023-05-31T16:32:50.898670Z"Pramanick, Soumita"https://zbmath.org/authors/?q=ai:pramanick.soumitaSummary: Radiative generation of realistic mixing in neutrino sector is studied at one-loop level in a scotogenic \(A 4 \times Z_2\) symmetric framework. A scheme of obtaining non-zero \(\theta_{13}\) through small mass splitting in right-handed neutrino sector is proposed. The model consists of three right-handed neutrinos, two of which were required to be degenerate in masses to yield the common structure of the left-handed neutrino mass matrix that corresponds to \(\theta_{13} = 0\), \(\theta_{23} = \pi/4\) and any \(\theta_{12}^0\) in particular the choices specific to the Tribimaximal (TBM), Bimaximal (BM) and Golden Ratio (GR) mixings. Non-zero \(\theta_{13}\), deviations of \(\theta_{23}\) from maximality and small corrections to the solar mixing angle \(\theta_{12}\) can be generated in one stroke by shifting from this degeneracy in the right-handed neutrino sector by a small amount. The lightest among the three \(Z_2\) odd inert \(SU(2)_L\) doublet scalars present in the model can be a potential dark matter candidate.Observational tests of the generalized uncertainty principle: Shapiro time delay, gravitational redshift, and geodetic precessionhttps://zbmath.org/1508.819922023-05-31T16:32:50.898670Z"Ökcü, Özgür"https://zbmath.org/authors/?q=ai:okcu.ozgur"Aydiner, Ekrem"https://zbmath.org/authors/?q=ai:aydiner.ekremSummary: This paper is based on the study of the paper of \textit{F. Scardigli} and \textit{R. Casadio} [``Gravitational tests of the generalized uncertainty principle'', Eur. Phys. J. C, Part. Fields 75, Article No. 425, 12 p. (2015; \url{doi:10.1140/epjc/s10052-015-3635-y})] where the authors computed the light deflection and perihelion precession for the Generalized Uncertainty Principle (GUP) modified Schwarzschild metric. In the present work, we computed the gravitational tests such as Shapiro time delay, gravitational redshift, and geodetic precession for the GUP modified Schwarzschild metric. Using the results of Solar system experiments and observations, we obtain upper bounds for the GUP parameter \(\beta\). Finally, we compare our bounds with other bounds in the literature.Supermassive black holeshttps://zbmath.org/1508.830012023-05-31T16:32:50.898670Z"King, Andrew"https://zbmath.org/authors/?q=ai:king.andrew-d|king.andrew-c|king.andrew-j.1|king.andrew-r|king.andrew-j-h|king.andrew-j|king.andrew-pPublisher's description: Written by an international leader in the field, this is a coherent and accessible account of the concepts that are now vital for understanding cutting-edge work on supermassive black holes. These include accretion disc misalignment, disc breaking and tearing, chaotic accretion, the merging of binary supermassive holes, the demographics of supermassive black holes, and the defining effects of feedback on their host galaxies. The treatment is largely analytic and gives in-depth discussions of the underlying physics, including gas dynamics, ideal and non-ideal magnetohydrodynamics, force-free electrodynamics, accretion disc physics, and the properties of the Kerr metric. It stresses aspects where conventional assumptions may be inappropriate and encourages the reader to think critically about current models. This volume will be useful for graduate or Masters courses in astrophysics, and as a handbook for active researchers in the field. eBook formats include colour figures while print formats are greyscale only.The irresistible attraction of gravity. A journey to discover black holeshttps://zbmath.org/1508.830032023-05-31T16:32:50.898670Z"Rezzolla, Luciano"https://zbmath.org/authors/?q=ai:rezzolla.lucianoPublisher's description: The mystery of gravity has captivated us for centuries. But what is gravity and how does it work? This engaging book delves into the bizarre and often counter-intuitive world of gravitational physics. Join distinguished astrophysicist Professor Luciano Rezzolla on this virtual journey into Einstein's world of gravity, with each milestone presenting ever more fascinating aspects of gravitation. Through gentle exposure to concepts such as spacetime curvature and general relativity, you will discover some of the most curious consequences of gravitational physics, such as black holes, neutron stars and gravitational waves. The author presents and explains one of the most impressive scientific achievements of recent times: the first image of a supermassive black hole. Written by one of the key scientists involved in producing these results, you'll get a behind-the-scenes view of how the image was captured and discover what happens to matter and light near a black hole.Spherical inhomogeneous solutions of Einstein and scalar-tensor gravity: a map of the landhttps://zbmath.org/1508.830052023-05-31T16:32:50.898670Z"Faraoni, Valerio"https://zbmath.org/authors/?q=ai:faraoni.valerio"Giusti, Andrea"https://zbmath.org/authors/?q=ai:giusti.andrea"Fahim, Bardia H."https://zbmath.org/authors/?q=ai:fahim.bardia-hSummary: We review spherical and inhomogeneous analytic solutions of the field equations of Einstein and of scalar-tensor gravity, including Brans-Dicke theory, non-minimally (possibly conformally) coupled scalar fields, Horndeski, and beyond Horndeski/DHOST gravity. The zoo includes both static and dynamic solutions, asymptotically flat, and asymptotically Friedmann-Lemaître-Robertson-Walker ones. We minimize overlap with existing books and reviews and we place emphasis on scalar field spacetimes and on geometries that are ``general'' within certain classes. Relations between various solutions, which have largely emerged during the last decade, are pointed out.The conformal Killing spinor initial data equationshttps://zbmath.org/1508.830062023-05-31T16:32:50.898670Z"Gasperín, E."https://zbmath.org/authors/?q=ai:gasperin.edgar"Williams, J. L."https://zbmath.org/authors/?q=ai:williams.jarrod-l|williams.j-l-m|williams.jason-l|williams.jessica-lynnThis paper considers the conformal vacuum Einstein equations on a globally hyperbolic four-dimensional manifold of signature \((1,3)\). The main result of this paper (Th.~3, p.~18) is that given a ``conformal Killing spinor initial data set'' (as defined p.~16) in some open set \(\mathcal U\) of a spacelike hypersurface, that satisfies either one of conditions (i) or (ii) of Lemma 3 (p.~18), then it may be continued into a solution of the conformal Einstein equations in some four-dimensional open set included in the domain of dependence of \(\mathcal U\), and this solution possesses a Killing spinor. The authors state that the condition that the initial hypersurface be spacelike may be relaxed to some extent (p.~3).
Reviewer: Satyanad Kichenassamy (Reims)New asymptotically flat static vacuum metrics with near Euclidean boundary datahttps://zbmath.org/1508.830072023-05-31T16:32:50.898670Z"An, Zhongshan"https://zbmath.org/authors/?q=ai:an.zhongshan"Huang, Lan-Hsuan"https://zbmath.org/authors/?q=ai:huang.lan-hsuanSummary: In our prior work toward Bartnik's static vacuum extension conjecture for near Euclidean boundary data, we establish a sufficient condition, called static regular, and confirm that large classes of boundary hypersurfaces are static regular. In this paper, we further improve some of those prior results. Specifically, we show that any hypersurface in an open and dense subfamily of a certain general smooth one-sided family of hypersurfaces (not necessarily a foliation) is static regular. The proof uses some of our new arguments motivated from studying the conjecture for boundary data near an arbitrary static vacuum metric.
{\copyright 2022 American Institute of Physics}Erratum to: ``Cosmology and gravitational waves in consistent \(D\rightarrow 4\) Einstein-Gauss-Bonnet gravity''https://zbmath.org/1508.830082023-05-31T16:32:50.898670Z"Aoki, Katsuki"https://zbmath.org/authors/?q=ai:aoki.katsuki"Gorji, Mohammad Ali"https://zbmath.org/authors/?q=ai:gorji.mohammad-ali"Mukohyama, Shinji"https://zbmath.org/authors/?q=ai:mukohyama.shinjiIn the authors' paper [ibid. 2020, No. 9, Paper No. 14, 18 p. (2020; Zbl 1493.83005)], the discussion about the observational bounds on the rescaled Gauss-Bonnet parameter in fifth and sixth (last) paragraphs in section 6, page 12 and 13 is changed.Quantum gravity and the square of Bell operatorshttps://zbmath.org/1508.830092023-05-31T16:32:50.898670Z"Aghababaei, S."https://zbmath.org/authors/?q=ai:aghababaei.s"Moradpour, H."https://zbmath.org/authors/?q=ai:moradpour.hooman"Shabani, H."https://zbmath.org/authors/?q=ai:shabani.hamidSummary: The Bell's inequality is a strong criterion to distinguish classical and quantum mechanical aspects of reality. Its violation is the net effect of the existence of non-locality in systems, an advantage for quantum mechanics over classical physics. The quantum mechanical world is under the control of the Heisenberg uncertainty principle that is generalized by quantum gravity scenarios, called generalized uncertainty principle (GUP). Here, the effects of GUP on the square of Bell operators of qubits and qutrits are studied. The achievements claim that the violation quality of the square of Bell inequalities may be a tool to get a better understanding of the quantum features of gravity. In this regard, it is obtained that the current accuracy of the Stern-Gerlach experiments implies upper bounds on the values of the GUP parameters.Generalized Ashtekar variables for Palatini \(f(\mathcal{R})\) modelshttps://zbmath.org/1508.830102023-05-31T16:32:50.898670Z"Bombacigno, Flavio"https://zbmath.org/authors/?q=ai:bombacigno.flavio"Boudet, Simon"https://zbmath.org/authors/?q=ai:boudet.simon"Montani, Giovanni"https://zbmath.org/authors/?q=ai:montani.giovanniSummary: We consider special classes of Palatini \(f(\mathcal{R})\) theories, featured by additional Loop Quantum Gravity inspired terms, with the aim of identifying a set of modified Ashtekar canonical variables, which still preserve the \(SU(2)\) gauge structure of the standard theory. In particular, we allow for affine connection to be endowed with torsion, which turns out to depend on the additional scalar degree affecting Palatini \(f(\mathcal{R})\) gravity, and in this respect we successfully construct a novel Gauss constraint. We analyze the role of the additional scalar field, outlining as it acquires a dynamical character by virtue of a non vanishing Immirzi parameter, and we describe some possible effects on the area operator stemming from such a revised theoretical framework. Finally, we compare our results with earlier studies in literature, discussing differences between metric and Palatini approaches. It is worth noting how the Hamiltonian turns out to be different in the two cases. The results can be reconciled when the analysis is performed in the Einstein frame.Nonlinear waves in magnetized quark matter and the reduced Ostrovsky equationhttps://zbmath.org/1508.830112023-05-31T16:32:50.898670Z"Fogaça, David A."https://zbmath.org/authors/?q=ai:fogaca.david-a"Sanches, S. M."https://zbmath.org/authors/?q=ai:sanches.s-m"Navarra, F. S."https://zbmath.org/authors/?q=ai:navarra.f-sSummary: We study nonlinear waves in a nonrelativistic ideal and cold quark gluon plasma immersed in a strong uniform magnetic field. In the context of nonrelativistic hydrodynamics with an external magnetic field we derive a nonlinear wave equation for baryon density perturbations, which can be written as a reduced Ostrovsky equation. We find analytical solutions and identify the effects of the magnetic field.Axion-radiation conversion by super and normal conductorshttps://zbmath.org/1508.830122023-05-31T16:32:50.898670Z"Iwazaki, Aiichi"https://zbmath.org/authors/?q=ai:iwazaki.aiichiSummary: We have proposed a method for the detection of dark matter axion. It uses superconductor under strong magnetic field. As is well known, the dark matter axion induces oscillating electric field under magnetic field. The electric field is proportional to the magnetic field and makes charged particles oscillate in conductors. Then, radiations of electromagnetic fields are produced. Radiation flux depends on how large the electric field is induced and how large the number of charged particles is present in the conductors. We show that the electric field in superconductor is essentially identical to the one induced in vacuum. It is proportional to the magnetic field. It is only present in the surface because of Meissner effect. On the other hand, although the magnetic field can penetrate the normal conductor, the oscillating electric field is only present in the surface of the conductor because of the skin effect. The strength of the electric field induced in the surface is equal to the one in vacuum. We obtain the electric field in the superconductor by solving equations of electromagnetic fields coupled with axion and Cooper pair described by Ginzburg-Landau model. The electric field in the normal conductor is obtained by solving equations of electromagnetic fields in the conductor coupled with axion. We compare radiation flux from the cylindrical superconductor with that from the normal conductor with same size. We find that the radiation flux from the superconductor is a hundred times larger than the flux from the normal conductor. We also show that when we use superconducting resonant cavity, we obtain radiation energy generated in the cavity two times of the order of the magnitude larger than that in normal conducting resonant cavity.Scalar dark matter and leptogenesis in the minimal scotogenic modelhttps://zbmath.org/1508.830132023-05-31T16:32:50.898670Z"Sarma, Lavina"https://zbmath.org/authors/?q=ai:sarma.lavina"Das, Pritam"https://zbmath.org/authors/?q=ai:das.pritam"Das, Mrinal Kumar"https://zbmath.org/authors/?q=ai:das.mrinal-kumarSummary: We study the minimal scotogenic model constituting an additional inert Higgs doublet and three sets of right-handed neutrinos. The scotogenic model connects dark matter, baryon asymmetry of the Universe and neutrino oscillation data. In our work, we obtain baryogenesis by the decay of TeV scale heavy neutral singlet fermion (\(N_2\)). We primarily focus on the intermediate-mass region of dark matter within \(M_W < M_{D M} \leq 550\) GeV, where observed relic density is suppressed due to co-annihilation processes. We consider thermal as well as the non-thermal approach of dark matter production and explore the possibility of the lightest stable candidate being a dark matter candidate. Within the inert Higgs doublet (IHD) desert, we explore a new allowed region of dark matter masses for the non-thermal generation of dark matter with a mass splitting of 10 GeV among the inert scalars. We also see the variation of relic abundance for unequal mass splitting among the scalars. The KamLand-Zen bound on the effective mass of the active neutrinos is also verified in this study.Gravitational constant model and correctionhttps://zbmath.org/1508.830142023-05-31T16:32:50.898670Z"Chen, Yu-Jie"https://zbmath.org/authors/?q=ai:chen.yujie"Li, Shi-Lin"https://zbmath.org/authors/?q=ai:li.shilin"Chen, Yu-Zhu"https://zbmath.org/authors/?q=ai:chen.yuzhu.1"Li, Wen-Du"https://zbmath.org/authors/?q=ai:li.wen-du"Dai, Wu-Sheng"https://zbmath.org/authors/?q=ai:dai.wushengSummary: We construct a model for considering the quantum correction of the gravitational constant. In the model, the gravitational constant originates from a coupling between the gravitational field and a scalar field. If the scalar field, as it should be in the real physical world, is a quantum field, the gravitational constant will have a quantum correction. The quantum correction, generally speaking, varies with spacetime coordinates. Therefore, the gravitational constant is no longer a constant. In different spacetime, the quantum correction is different, for the coupling in different spacetime is different. As a result, the gravitational constant in different spacetime is different, though the difference is only at the quantum level. We calculate the quantum correction of the gravitational constant in the Schwarzschild spacetime, the \(H_3\) (Euclidean \(AdS_3\)) spacetime, the \(H_3/Z\) spacetime, the universe model, the de Sitter spacetime, and the Rindler spacetime.
{\copyright 2022 American Institute of Physics}A scattering theory for the wave equation on Kerr black hole exteriorshttps://zbmath.org/1508.830152023-05-31T16:32:50.898670Z"Dafermos, Mihalis"https://zbmath.org/authors/?q=ai:dafermos.mihalis"Rodnianski, Igor"https://zbmath.org/authors/?q=ai:rodnianski.igor"Shlapentokh-Rothman, Yakov"https://zbmath.org/authors/?q=ai:shlapentokh-rothman.yakovSummary: We develop a definitive physical-space scattering theory for the scalar wave equation \(\square_g\psi=0\) on Kerr exterior backgrounds in the general subextremal case \(|a|<M\). In particular, we prove results corresponding to ``existence and uniqueness of scattering states'' and ``asymptotic completeness'' and we show moreover that the resulting ``scattering matrix'' mapping radiation fields on the past horizon \(\mathcal{H}^-\) and past null infinity \(\mathcal{I}^-\) to radiation fields on \(\mathcal{H}^+\) and \(\mathcal{I}^+\) is a bounded operator. The latter allows us to give a time-domain theory of superradiant reflection. The boundedness of the scattering matrix shows in particular that the maximal amplification of solutions associated to ingoing finite-energy wave packets on past null infinity \(\mathcal{I}^-\) is bounded. On the frequency side, this corresponds to the novel statement that the suitably normalized reflection and transmission coefficients are uniformly bounded independently of the frequency parameters. We further complement this with a demonstration that superradiant reflection indeed amplifies the energy radiated to future null infinity \(\mathcal{I}^+\) of suitable wave-packets as above. The results make essential use of a refinement of our recent proof [Ann. Math. (2) 183, No. 3, 787--913 (2016; Zbl 1347.83002)] of boundedness and decay for solutions of the Cauchy problem so as to apply in the class of solutions where only a degenerate energy is assumed finite. We show in contrast that the analogous scattering maps cannot be defined for the class of finite non-degenerate energy solutions. This is due to the fact that the celebrated horizon red-shift effect acts as a blue-shift instability when solving the wave equation backwards.Integrable \(\lambda\)-deformations of the Euclidean black stringhttps://zbmath.org/1508.830162023-05-31T16:32:50.898670Z"Driezen, Sibylle"https://zbmath.org/authors/?q=ai:driezen.sibylle"Sfetsos, Konstantinos"https://zbmath.org/authors/?q=ai:sfetsos.konstantinosSummary: Non-trivial outer algebra automorphisms may be utilized in \(\lambda \)-deformations of (gauged) WZW models thus providing an efficient way to construct new integrable models. We provide two such integrable deformations of the exact coset CFT \(SU(2)_k \times U(1)/U(1)_q\) with a vector and axial residual gauge. Besides the integer level \(k\) and the deformation parameter \(\lambda\), these models are characterized by the embedding parameter \(q\) of the \(U(1)\) factor. We show that an axial-vector T-duality persists along the deformations and, therefore, the models are canonically equivalent. We demonstrate integrability even though the space is non-symmetric and compute the \textit{RG}-flow equations for the parameters \(\lambda\) and \(q\). Our example provides an integrable deformation of the gravitational solution representing a Euclidean three-dimensional black string.Asymptotic charges for spin-1 and spin-2 fields at the critical sets of null infinityhttps://zbmath.org/1508.830172023-05-31T16:32:50.898670Z"Ali Mohamed, Mariem Magdy"https://zbmath.org/authors/?q=ai:ali-mohamed.mariem-magdy"Valiente Kroon, Juan A."https://zbmath.org/authors/?q=ai:valiente-kroon.juan-antonioSummary: The asymptotic charges of spin-1 and spin-2 fields are studied near spatial infinity. We evaluate the charges at the critical sets where spatial infinity meets null infinity with the aim of finding the relation between the charges at future and past null infinities. To this end, we make use of Friedrich's framework of the cylinder at spatial infinity to obtain asymptotic expansions of the Maxwell and spin-2 fields near spatial infinity, which are fully determined in terms of initial data on a Cauchy hypersurface. With expanding the initial data in terms of spin-weighted spherical harmonics, it is shown that only a subset of the initial data, which satisfy certain regularity conditions, gives rise to well-defined charges at the point where future (past) infinity meets spatial infinity. Given such initial data, the charges are shown to be fully expressed in terms of the freely specifiable part of the data. Moreover, it is shown that there exists a natural correspondence between the charges defined at future and past null infinities.
{\copyright 2022 American Institute of Physics}On the discrete Dirac spectrum of a point electron in the zero-gravity Kerr-Newman spacetimehttps://zbmath.org/1508.830182023-05-31T16:32:50.898670Z"Kiessling, Michael K.-H."https://zbmath.org/authors/?q=ai:kiessling.michael-karl-heinz"Ling, Eric"https://zbmath.org/authors/?q=ai:ling.eric"Tahvildar-Zadeh, A. Shadi"https://zbmath.org/authors/?q=ai:tahvildar-zadeh.a-shadiSummary: The discrete spectrum of the Dirac operator for a point electron in the maximal analytically extended Kerr-Newman spacetime is determined in the zero-\(G\) limit (z\(G\)KN), under some restrictions on the electrical coupling constant and on the radius of the ring-singularity of the z\(G\)KN spacetime. The spectrum is characterized by a triplet of integers, associated with winding numbers of orbits of dynamical systems on cylinders. A dictionary is established that relates the spectrum with the known hydrogenic Dirac spectrum. Numerical illustrations are presented. Open problems are listed.
{\copyright 2022 American Institute of Physics}Two-dimensional Lifshitz-like AdS black holes in \(F(R)\) gravityhttps://zbmath.org/1508.830192023-05-31T16:32:50.898670Z"Eslam Panah, B."https://zbmath.org/authors/?q=ai:eslam-panah.bSummary: Two-dimensional (2D) Lifshitz-like black holes in special \(F(R)\) gravity cases are extracted. We indicate an essential singularity at \(r = 0\), covered by an event horizon. Then, conserved and thermodynamic quantities, such as temperature, mass, entropy, and the heat capacity of 2D Lifshitz-like black holes in \(F(R)\) gravity, are evaluated. Our analysis shows that 2D Lifshitz-like black hole solutions can be physical solutions, provided that the cosmological constant is negative (\(\Lambda < 0\)). Indeed, there is a phase transition between stable and unstable cases by increasing the radius of AdS black holes. In other words, the 2D Lifshitz-like AdS black holes with large radii are physical and enjoy thermal stability. The obtained 2D Lifshitz-like AdS-black holes in \(F(R)\) gravity turn into the well-known 2D Schwarzschild AdS-black holes when the Lifshitz-like parameter is zero (\(s = 0\)). Moreover, correspondence between these black hole solutions and the 2D rotating black hole solutions is found by adjusting the Lifshitz-like parameter.
{\copyright 2022 American Institute of Physics}\(k\)-Inflation-corrected Einstein-Gauss-Bonnet gravity with massless primordial gravitonshttps://zbmath.org/1508.830202023-05-31T16:32:50.898670Z"Odintsov, S. D."https://zbmath.org/authors/?q=ai:odintsov.sergei-d"Oikonomou, V. K."https://zbmath.org/authors/?q=ai:oikonomou.vasilis-k"Fronimos, F. P."https://zbmath.org/authors/?q=ai:fronimos.f-pSummary: In the present paper, we study the inflationary phenomenology of a \(k\)-inflation corrected Einstein-Gauss-Bonnet theory. Non-canonical kinetic terms are known for producing Jean instabilities or superluminal sound wave velocities in the aforementioned era, but we demonstrate in this work that by adding Gauss-Bonnet string corrections and assuming that the non-canonical kinetic term \(\omega X^\gamma\) is in quadratic, one can obtain a ghost free description. Demanding compatibility with the recent GW170817 event forces one to accept that the relation \(\ddot{\xi} = H \dot{\xi}\) for the scalar coupling function \(\xi(\phi)\). As a result, the scalar functions of the theory are revealed to be interconnected and by assuming a specific form for one of them, specifies immediately the other. Here, we shall assume that the scalar potential is directly derivable from the equations of motion, once the Gauss-Bonnet coupling is appropriately chosen, but obviously the opposite is feasible as well. As a result, each term entering the equations of motion, can be written in terms of the scalar field and a relatively tractable phenomenology is produced. For quadratic kinetic terms, the resulting scalar potential is quite elegant functionally. Different exponents, which lead to either a more perplexed solution for the scalar potential, are still a possibility which was not further studied. We also discuss in brief the non-Gaussianities issue under the slow-roll and constant-roll conditions holding true, and we demonstrate that the predicted amount of non-Gaussianities is significantly enhanced in comparison to the \(k\)-inflation free Einstein-Gauss-Bonnet theory.Energy conditions in a modified Brans-Dicke theoryhttps://zbmath.org/1508.830212023-05-31T16:32:50.898670Z"Amani, Hootan"https://zbmath.org/authors/?q=ai:amani.hootan"Halpern, Paul"https://zbmath.org/authors/?q=ai:halpern.paulSummary: We consider a modified version of Brans-Dicke theory (MBDT) in four dimensions (4D) obtained by applying the induced matter method of Wesson to a 5D generalized Brans-Dicke theory. In 5D the model consists of pure vacuum, with no self-interacting potential, except for a scalar field. Following Wesson's protocol, we group geometric terms in the 5D Einstein tensor arising from the extra dimension, move them to the other side of the generalized field equations, and identify them as the energy-momentum of the induced matter in 4D. Thus the extra dimension in 5D leads naturally to an effective matter field in 4D. Constraining the 5D geometry to be a generalization of the anisotropic Bianchi type I universe model first studied by Kasner, we derive the induced energy-momentum in MBDT and apply it to the investigation of energy conditions. The specified induced energy-momentum of that MBDT model consists of the energy density and directional pressure which indicate the anisotropy of the universe. We discuss the energy conditions and their bounds in the MBDT with such an induced imperfect fluid, with an eye toward a realistic model of the present-day universe, and consider the large-scale behavior of that spatially homogeneous and anisotropic model. We discuss how the energy conditions would be satisfied or violated in the context of MBDT, with the aim of providing a feasible description of the universe in the current era.Hidden symmetries of two-field cosmological modelshttps://zbmath.org/1508.830222023-05-31T16:32:50.898670Z"Anguelova, Lilia"https://zbmath.org/authors/?q=ai:anguelova.lilia"Babalic, Elena Mirela"https://zbmath.org/authors/?q=ai:babalic.elena-mirela"Lazaroiu, Calin Iuliu"https://zbmath.org/authors/?q=ai:lazaroiu.calin-iuliuSummary: We determine the most general time-independent Noether symmetries of two-field cosmological models with rotationally-invariant scalar manifold metrics. In particular, we show that such models can have hidden symmetries, which arise if and only if the scalar manifold metric has Gaussian curvature \(-3/8\), i.e. when the model is of elementary \(\alpha\)-attractor type with a fixed value of the parameter \(\alpha\). In this case, we find explicitly all scalar potentials compatible with hidden Noether symmetries, thus classifying all models of this type. We also discuss some implications of the corresponding conserved quantity.The space of light rays: causality and \(L\)-boundaryhttps://zbmath.org/1508.830232023-05-31T16:32:50.898670Z"Bautista, A."https://zbmath.org/authors/?q=ai:bautista.alfredo"Ibort, A."https://zbmath.org/authors/?q=ai:ibort.alberto"Lafuente, J."https://zbmath.org/authors/?q=ai:lafuente.javierSummary: The space of light rays \(\mathcal{N}\) of a conformal Lorentz manifold \((M,\mathcal{C})\) is, under some topological conditions, a manifold whose basic elements are unparametrized null geodesics. This manifold \(\mathcal{N}\), strongly inspired on R. Penrose's twistor theory, keeps all information of \(M\) and it could be used as a space complementing the spacetime model. In the present review, the geometry and related structures of \(\mathcal{N}\), such as the space of skies \(\varSigma\) and the contact structure \(\mathcal{H}\), are introduced. The causal structure of \(M\) is characterized as part of the geometry of \(\mathcal{N}\). A new causal boundary for spacetimes \(M\) prompted by R. Low, the \(L\)-boundary, is constructed in the case of 3-dimensional manifolds \(M\) and proposed as a model of its construction for general dimension. Its definition only depends on the geometry of \(\mathcal{N}\) and not on the geometry of the spacetime \(M\). The properties satisfied by the \(L\)-boundary \(\partial M\) permit to characterize the obtained extension \(\overline{M}=M\cup\partial M\) and this characterization is also proposed for general dimension.Gravitational constraints on a lightlike boundaryhttps://zbmath.org/1508.830242023-05-31T16:32:50.898670Z"Canepa, G."https://zbmath.org/authors/?q=ai:canepa.giovanni"Cattaneo, A. S."https://zbmath.org/authors/?q=ai:cattaneo.alberto-sergio"Tecchiolli, M."https://zbmath.org/authors/?q=ai:tecchiolli.manuelSummary: We analyse the boundary structure of general relativity in the coframe formalism in the case of a lightlike boundary, i.e. when the restriction of the induced Lorentzian metric to the boundary is degenerate. We describe the associated reduced phase space in terms of constraints on the symplectic space of boundary fields. We explicitly compute the Poisson brackets of the constraints and identify the first- and second-class ones. In particular, in the \(3+1\)-dimensional case, we show that the reduced phase space has two local degrees of freedom, instead of the usual four in the non-degenerate case.De Sitter and power-law solutions in non-local Gauss-Bonnet gravityhttps://zbmath.org/1508.830262023-05-31T16:32:50.898670Z"Elizalde, E."https://zbmath.org/authors/?q=ai:elizalde.emilio"Odintsov, S. D."https://zbmath.org/authors/?q=ai:odintsov.sergei-d"Pozdeeva, E. O."https://zbmath.org/authors/?q=ai:pozdeeva.ekaterina-o"Vernov, S. Yu."https://zbmath.org/authors/?q=ai:vernov.sergey-yuSummary: The cosmological dynamics of a non-locally corrected gravity theory, involving a power of the inverse d'Alembertian, is investigated. Casting the dynamical equations into local form, the fixed points of the models are derived, as well as corresponding de Sitter and power-law solutions. Necessary and sufficient conditions on the model parameters for the existence of de Sitter solutions are obtained. The possible existence of power-law solutions is investigated, and it is proven that models with de Sitter solutions have no power-law solutions. A model is found, which allows to describe the matter-dominated phase of the Universe evolution.QFT and topology in two dimensions: \( \operatorname{SL}(2, \mathbb{R})\)-symmetry and the de Sitter universehttps://zbmath.org/1508.830272023-05-31T16:32:50.898670Z"Epstein, Henri"https://zbmath.org/authors/?q=ai:epstein.henri"Moschella, Ugo"https://zbmath.org/authors/?q=ai:moschella.ugoSummary: We study bosonic quantum field theory on the double covering \(\widetilde{dS}_2\) of the two-dimensional de Sitter universe, identified to a coset space of the group \(\operatorname{SL}(2, \mathbb{R})\). The latter acts effectively on \(\widetilde{dS}_2\) and can be interpreted as it relativity group. The manifold is locally identical to the standard the Sitter spacetime \({dS}_2\); it is globally hyperbolic, geodesically complete and an inertial observer sees exactly the same bifurcate Killing horizons as in the standard one-sheeted case. The different global Lorentzian structure causes, however, drastic differences between the two models. We classify all the \(\operatorname{SL}(2, \mathbb{R})\)-invariant two-point functions and show that: (1) there is no Hawking-Gibbons temperature; (2) there is no covariant field theory solving the Klein-Gordon equation with mass less than \(1/2R\) , i.e., the complementary fields go away.The solution space of the Einstein's vacuum field equations for the case of five-dimensional Bianchi type I (type \(4A_1\))https://zbmath.org/1508.830292023-05-31T16:32:50.898670Z"Pailas, T."https://zbmath.org/authors/?q=ai:pailas.t"Terzis, Petros A."https://zbmath.org/authors/?q=ai:terzis.petros-a"Christodoulakis, T."https://zbmath.org/authors/?q=ai:christodoulakis.theodosiosSummary: We consider the 4+1 Einstein's field equations (EFE's) in vacuum, simplified by the assumption that there is a 4D sub-manifold on which an isometry group of dimension four acts simply transitive. In particular, we consider the abelian group type \(4A_1\); and thus the emerging homogeneous sub-space is flat. Through the use of coordinate transformations that preserve the sub-manifold's manifest homogeneity, a coordinate system is chosen in which the shift vector is zero. The resulting equations remain form invariant under the action of the constant automorphisms group. This group is used in order to simplify the equations and obtain their complete solution space which consists of seven families corresponding to 21 distinct solutions. Apart form the Kasner type all the other solutions found are, to the best of our knowledge, new. Some of them correspond to cosmological solutions, others seem to depend on some spatial coordinate and there are also pp-wave solutions.Wavefunction of the universe: reparametrization invariance and field redefinitions of the minisuperspace path integralhttps://zbmath.org/1508.830302023-05-31T16:32:50.898670Z"Partouche, Hervé"https://zbmath.org/authors/?q=ai:partouche.herve"Toumbas, Nicolaos"https://zbmath.org/authors/?q=ai:toumbas.nicolaos"de Vaulchier, Balthazar"https://zbmath.org/authors/?q=ai:de-vaulchier.balthazarThe initial singularity of cosmology and the transition to an inflationary evolution are fundamental questions expected to be answered by a successful quantum gravity model. The careful analysis in this paper considers a mini-superspace wavefunction of a closed homogeneous and isotropic universe with a cosmological constant as only source term. The authors construct the quantum state as a Euclidean path integral satisfying the no boundary condition. We discuss the reparametrization properties of both the time coordinate and the cosmic scale factor. The path integral is solved with the steepest descent approximation. The time transformation leads to gauge-invariant predictions, while the wavefunction for different choices of the scale factor parametrization get identical predictions only in the semiclassical approximation. Its applicability for the considered problem however seems problematic. The paper delivers a certain intermediate step in overcoming the fundamental problems raised by the big-bang singularity for cosmology. The inclusion of sources as scalar fields in the action will allow more realistic predictions for quantum cosmology.
Reviewer: Volker Müller (Potsdam)Electrically charged strange quark stars with anisotropic matter: exact analytical solutionhttps://zbmath.org/1508.850012023-05-31T16:32:50.898670Z"Panotopoulos, Grigoris"https://zbmath.org/authors/?q=ai:panotopoulos.grigoris"Lopes, Ilídio"https://zbmath.org/authors/?q=ai:lopes.ilidioSummary: We obtain a new exact analytical solution to the Einstein-Maxwell field equations with anisotropic matter. The solution describes the interior of anisotropic, electrically charged strange quark stars with a nonlinear equation-of-state. We show the behavior of the solution graphically, and we determine the properties of the star (radius, mass, electric charge and compactness) for specific numerical values of the parameters involved. Finally, we check that causality is not violated, and that the energy conditions, the upper bound on the compactness of the stars, and constraints on the mass of the objects coming from observed massive pulsars and direct detection of gravitational waves are all fulfilled.