Abstract

In singularity generating spacetimes both the out-going and ingoing expansions of null geodesic congruences + and − 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 = − equation of state near r = 0. By following both the expansion parameters + and − across the horizon and into the black hole we find that both + and + − have turning points inside the trapped region. Further, we find that deep inside the black hole there is a region 0 ≤ r < r0 (that includes the black hole center) which is not trapped. Thus the trapped region is bounded both from outside and inside. The spacetime is geodetically complete, a result which violates a condition for singularity formation. It is inferred that in general if gravitational collapse were to proceed with a p = − fluid formation, the resulting black hole may be singularity-free.

Publication Date

2008

Comments

Also archived in: arXiv:0708.2360 v1 Aug 17 2007Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type

Article

Department, Program, or Center

School of Physics and Astronomy (COS)

Campus

RIT – Main Campus

Share

COinS