×

Gravitational collapse in General Relativity and in \(R^2\)-gravity: a comparative study. (English) Zbl 1426.83023

Summary: We compare the gravitational collapse of homogeneous perfect fluid with various equations of state in the framework of General Relativity and in \(R^2\) gravity. We make our calculations using dimensionless time with characteristic timescale \(t_g \sim(G \rho)^{- 1 / 2}\), where \(\rho\) is a density of collapsing matter. The cases of matter, radiation and stiff matter are considered. We also account the possible existence of vacuum energy and its influence on gravitational collapse. In a case of \(R^2\) gravity, we have additional degree of freedom for initial conditions of collapse. For barotropic equation of state (EoS) \(p = w \rho\), the result depends from the value of parameter \(w\): for \(w > 1 / 3\) the collapse occurs slowly in comparison with General Relativity while for \(w < 1 / 3\), we have the opposite situation. Vacuum energy as expected slows down the rate of collapse and for some critical density gravitational contraction may change to expansion. It is interesting to note that for General Relativity such expansion is impossible. We also consider the collapse in the presence of so-called phantom energy. For description of phantom energy, we use Lagrangian in the form \(- X - V\) (where \(X\) and \(V\) are the kinetic and potential energy of the field, respectively) and consider the corresponding Klein-Gordon equation for phantom scalar field.

MSC:

83C75 Space-time singularities, cosmic censorship, etc.
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
76E20 Stability and instability of geophysical and astrophysical flows
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81T10 Model quantum field theories
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C47 Methods of quantum field theory in general relativity and gravitational theory
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Oppenheimer, J. R. and Snyder, H., On continued gravitational contraction, Phys. Rev.56 (1939) 455-459. · Zbl 0022.28104
[2] Weinberg, S., Gravitation and Cosmology (John Wiley and Sons, Inc., 1972).
[3] Schutz, B. F., A First Course in General Relativity (Cambridge University Press, 1985). · Zbl 0556.53040
[4] Wald, R. M., General Relativity (The University of Chicago Press, 1984). · Zbl 0549.53001
[5] Abbott, B. P.et al., Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett.116 (2016) 061102.
[6] Liddle, A. R., An Introduction to Modern Cosmology, 2nd edn. (John Wiley and Sons, 2003).
[7] Guth, A. H., Inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D23 (1981) 347-356. · Zbl 1371.83202
[8] Perlmutter, S.et al., Measurements of omega and lambda from 42 high-redshift supernovae, Astrophys. J.517 (1999) 565-586. · Zbl 1368.85002
[9] Riess, A. G.et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J.166 (1998) 1009-1038.
[10] Einstein, A., Cosmological considerations in the general theory of relativity, Sitzungsber. Preuss. Akad. Wiss. Phys.-Math. Klasse6 (1917) 142-152. · JFM 46.1295.01
[11] Kowalski, M.et al., Improved cosmological constraints from new, old and combined supernova datasets, Astrophys. J.686 (2008) 749-778.
[12] Ade, P. A. R.et al., Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys.594 (2016) A13.
[13] Weinberg, S., The cosmological constant problem, Rev. Mod. Phys.61 (1989) 1-23. · Zbl 1129.83361
[14] Linde, A., A brief history of the multiverse, Reports Progress Phys.80 (2017) 022001.
[15] Caldwell, R. R., Kamionkowski, M. and Weinberg, N. N., Phantom energy: Dark energy with \(w < - 1\) causes a cosmic doomsday, Phys. Rev. Lett.91 (2003) 071301.
[16] Steinhardt, P., Wang, L. and Zlatev, I., Cosmological tracking solutions, Phys. Rev. D59 (1999) 123504.
[17] Hu, Y., Li, M., Li, N. and Zhang, Z., Holographic dark energy with cosmological constant, J. Cosmol. Astropart. Phys.08 (2015) 012.
[18] Nojiri, S. and Odintsov, S. D., Quantum de Sitter cosmology and phantom matter, Phys. Lett. B562 (2003) 147-152. · Zbl 1027.83543
[19] Singh, P., Sami, M. and Dadhich, N., Cosmological dynamics of phantom field, Phys. Rev. D68 (2003) 023522.
[20] Sami, M. and Toporensky, A., Phantom field and the fate of the universe, Mod. Phys. Lett. A19 (2004) 1509-1517.
[21] Nojiri, S. and Odintsov, S. D., Unified cosmic history in modified gravity: From \(F(R)\) theory to Lorentz non-invariant models, Phys. Rep.505 (2011) 59-144.
[22] Capozziello, S. and Faraoni, V., Beyond Einstein Gravity (Springer, New York, 2010). · Zbl 1206.85001
[23] Capozziello, S. and De Laurentis, M., Extended theories of gravity, Phys. Rep.509 (2011) 167-321.
[24] de la Cruz-Dombriz, A. and Saez-Gomez, D., Black holes, cosmological solutions, future singularities, and their thermodynamical properties in modified gravity theories, Entropy14 (2012) 1717-1770. · Zbl 1297.83018
[25] Nojiri, S., Odintsov, S. D. and Oikonomu, V. K., Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution, Phys. Rep.692 (2017) 1-104. · Zbl 1370.83084
[26] Harko, T., Lobo, S. N. F., Nojiri, S. and Odintsov, S. D., \(f(R, T)\) gravity, Phys. Rev. D84 (2011) 024020.
[27] Uzan, J., Cosmological scaling solutions of non minimally coupled scalar fields, Phys. Rev. D59 (1999) 123510.
[28] Chiba, T., Quintessence, the gravitational constant, and gravity, Phys. Rev. D60 (1999) 083508.
[29] Nojiri, S. and Odintsov, S. D., Modified Gauss-Bonnet theory as gravitational alternative for dark energy, Phys. Lett. B631 (2005) 1-6. · Zbl 1247.83292
[30] Nojiri, S., Odintsov, S. D. and Sasaki, M., Gauss-Bonnet dark energy, Phys. Rev. D71 (2005) 123509. · Zbl 1247.83292
[31] Goldswirth, D. S. and Piran, T., Gravitational collapse of massless scalar field and cosmic censorship, Phys. Rev. D36 (1987) 3575.
[32] Shapiro, S. L. and Teukolsky, S. A., Gravitational collapse of rotating spheroids and the formation of naked singularities, Phys. Rev. D45 (1992) 2006-2012.
[33] Joshi, P. S., Goswami, R. and Dadhich, N., Why do naked singularities form in gravitational collapse? II, Phys. Rev. D70 (2004) 087502.
[34] Giambo, R., Gravitational collapse of homogeneous scalar fields, Class. Quantum Gravit.22 (2005) 2295-2305. · Zbl 1097.83022
[35] Goswami, R. and Joshi, P. S., Gravitational collapse of a self-interacting scalar field, Mod. Phys. Lett. A22 (2007) 65-74. · Zbl 1203.83035
[36] Ganguly, K. and Banerjee, N., Spherically symmetric scalar field collapse, Pramana80 (2013) 439-448.
[37] Joshi, P. S., Malafarina, D. and Narayan, R., Distinguishing black holes from naked singularities through their accretion disk properties, Class. Quantum Gravit.31 (2014) 015002. · Zbl 1287.83032
[38] Baier, R., Nishimura, H. and Stricker, S. A., Scalar field collapse with negative cosmological constant, Class. Quantum Gravit.32 (2015) 135021. · Zbl 1327.83194
[39] Azam, M., Bhatt, J. R. and Sami, M., Many-body aspects of gravity in compact stars, Phys. Scripta93 (2018) 025001.
[40] Sharif, M. and Kausar, H. R., Gravitational perfect fluid collapse in \(f(R)\) gravity, Astrophys. Space Sci.331 (2011) 281-288. · Zbl 1209.83034
[41] Cembranos, J. A. R., de la Cruz-Dombriz, A. and Montes, B. N., Gravitational collapse in \(f(R)\) theories, J. Cosmol. Astropart. Phys.04 (2012) 021.
[42] E. Santos, Can modified gravity prevent the gravitational collapse to black hole? preprint (2011), arXiv:1112.4997 [gr-qc].
[43] Ghosh, S. G. and Maharaj, S. D., Gravitational collapse of null dust in \(f(R)\) gravity, Phys. Rev. D85 (2012) 124064.
[44] Bamba, K., Nojiri, S. and Odintsov, S. D., Time-dependent matter instability and star singularity in \(f(R)\) gravity, Phys. Lett. B698 (2011) 451-456.
[45] Arbuzova, E. V. and Dolgov, A. D., Explosive phenomena in modified gravity, Phys. Lett. B700 (2011) 289-293.
[46] Amir, M. J. and Ali, S., Spherical symmetric gravitational collapse in Chern-Simon modified gravity, Int. J. Theor. Phys.55 (2016) 2040-2052. · Zbl 1338.83136
[47] A. Bonanno, B. Koch and A. Platania, Gravitational collapse in quantum Einstein gravity, preprint (2017), arXiv:1710.10845 [gr-qc]. · Zbl 1411.83020
[48] Ratra, B. and Peebles, P. J. E., Cosmological consequences of a rolling homogeneous scalar field, Phys. Rev. D37 (1988) 3406-3427.
[49] Zlatev, I., Wang, L. M. and Steinhardt, P. J., Quintessence, cosmic coincidence, and the cosmological constant, Phys. Rev. Lett.82 (1999) 896-899.
[50] Linde, A. D., Chaotic inflation, Phys. Lett. B129 (1983) 177-181.
[51] Linde, A. D., Inflation and Quantum Cosmology (Academic Press, 1990). · Zbl 0692.53028
[52] Kallosh, R., Kratochvil, J., Linde, A., Linder, E. V. and Shmakova, M., Observational bounds on cosmic doomsday, J. Cosmol. Astropart. Phys.10 (2003) 015.
[53] Harko, T. and Mak, M. K., Integrability cases for the anharmonic oscillator equation, J. Pure Appl. Math.10 (2013) 115-129.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.