Can gravitational collapse sustain singularity-free trapped surfaces?

Details Can gravitational collapse sustain singularity-free trapped surfaces? Can gravitational collapse sustain singularity-free trapped surfaces?

2007-08-17

arxiv.org/abs/0708.2360v1

Int.J.Mod.Phys.D17:165-177,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, 3 figures, accepted for publication in International Journal of Modern Physics D

Scientific paper

10.1142/S0218271808011924

In singularity generating spacetimes both the out-going and in-going expansions of null geodesic congruences $\theta ^{+}$ and $\theta ^{-}$ should become increasingly negative without bound, inside the horizon. This behavior leads to geodetic incompleteness which in turn predicts the existence of a singularity. In this work we inquire on whether, in gravitational collapse, spacetime can sustain singularity-free trapped surfaces, in the sense that such a spacetime remains geodetically complete. As a test case, we consider a well known solution of the Einstien Field Equations which is Schwarzschild-like at large distances and consists of a fluid with a $p=-\rho $ equation of state near $r=0$. By following both the expansion parameters $\theta ^{+}$ and $\theta ^{-}$ across the horizon and into the black hole we find that both $\theta ^{+}$ and $\theta ^{+}\theta ^{-}$ have turning points inside the trapped region. Further, we find that deep inside the black hole there is a region $0\leq r

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