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Nakedly singular counterpart of Schwarzschild’s incompressible star. A barotropic continuity condition in the center. (English) Zbl 1434.83084
Summary: A static sphere of incompressible fluid with uniform proper energy density is considered as an example of exact star-like solution with weakened central regularity conditions characteristic of a nakedly singular spherical vacuum solution. The solution is a singular counterpart of the Schwarzschild’s interior solution. The initial condition in the center for general barotropic equations of state is established.
83C75 Space-time singularities, cosmic censorship, etc.
83C57 Black holes
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C15 Exact solutions to problems in general relativity and gravitational theory
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
NP; NPspinor
Full Text: DOI
[1] Carminati, J.; Mclenaghan, Rg, Algebraic invariants of the Riemann tensor in a four-dimensional Lorentzian space, J. Math. Phys., 32, 3135-3140 (1991) · Zbl 0736.76081
[2] Oppenheimer, Jr; Volkoff, Gm, On massive neutron cores, Phys. Rev., 55, 374-381 (1939) · Zbl 0020.28501
[3] Misner, Cw; Sharp, Dh, Relativistic equations for adiabatic, spherically symmetric gravitational collapse, Phys. Rev., 136, B571-B576 (1964) · Zbl 0129.41102
[4] Wald, Rm, General Relativity (1984), Chicago: Chicago Univ. Pr, Chicago · Zbl 0549.53001
[5] Joshi, Pankaj S., Gravitational Collapse and Spacetime Singularities. Cambridge Monographs on Mathematical Physics (2012), Cambridge: Cambridge University Press, Cambridge · Zbl 1246.83012
[6] Joshi, Ps; Malafarina, D.; Narayan, R., Equilibrium configurations from gravitational collapse, Class. Quantum Gravity, 28, 23, 235018 (2011) · Zbl 1231.83024
[7] Malafarina, D.; Joshi, Ps, Gravitational collapse with tangential pressure, Int. J. Mod. Phys. D, 20, 463-495 (2011) · Zbl 1220.83035
[8] Joshi, Ps; Malafarina, D., Recent developments in gravitational collapse and spacetime singularities, Int. J. Mod. Phys. D, 20, 2641-2729 (2011) · Zbl 1263.83011
[9] Joshi, Ps; Malafarina, D.; Saraykar, Rv, Genericity aspects in gravitational collapse to black holes and naked singularities, Int. J. Mod. Phys. D, 21, 8, 1250066 (2012) · Zbl 1277.83069
[10] Joshi, Ps; Malafarina, D., Instability of black hole formation under small pressure perturbations, Gen. Relativ. Gravit., 45, 2, 305-317 (2013) · Zbl 1261.83026
[11] Joshi, Ps; Malafarina, D.; Narayan, R., Distinguishing black holes from naked singularities through their accretion disc properties, Class. Quantum Gravity, 31, 1, 015002 (2013) · Zbl 1287.83032
[12] Woszczyna, A.; Kutschera, M.; Kubis, S.; Czaja, W.; Plaszczyk, P.; Golda, Za, Nakedly singular non-vacuum gravitating equilibrium states, Gen. Relativ. Gravit., 48, 1, 5 (2015) · Zbl 1332.83030
[13] Tolman, Rc, Static solutions of Einstein’s field equations for spheres of fluid, Phys. Rev., 55, 364-373 (1939) · Zbl 0020.28407
[14] Schwarzschild, K.: Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie. Preussische Akademie der Wissenschaften, Sitzungsberichte, 1916 (Erster Halbband), Berlin (1916) · JFM 46.1297.01
[15] Mazur, Po; Mottola, E., Surface tension and negative pressure interior of a non-singular black hole, Class. Quantum Gravity, 32, 21, 215024 (2015) · Zbl 1329.83120
[16] Gradshteyn, Is; Ryzhik, Im, Table of Integrals, Series, and Products (2015), Amsterdam: Elsevier, Amsterdam · Zbl 0918.65002
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