Abstract
Black holes are classically characterized by event horizon which is the boundary of the region from which particles or photons can escape to infinity in the future direction. Unfortunately this characterization is a global concept as the knowledge of the whole spacetime is needed in order to locate a black hole region and the event horizon. It is therefore important to recognize black holes locally; this has motivated the need to use local approach to characterize black holes. Specifically, we apply covariant divergence and Gauss’s divergence theorems to compute the divergences and the fluxes of appropriate null vectors in the Kerr spacetime to actually determine the existence of trapped and marginally trapped surfaces in its black hole region.
Highlights
One of the most striking results of General Relativity is its prediction of black holes which are spacetime regions from which no signal can be seen by an observer far from the matter sources (Frolov and Zelnikov, 2011)
Black holes are classically characterized by event horizon which is the boundary of the region from which particles or photons can escape to infinity in the future direction
General relativity shows that black holes are remarkably simple objects which are characterized by just a few numbers
Summary
One of the most striking results of General Relativity is its prediction of black holes which are spacetime regions from which no signal can be seen by an observer far from the matter sources (Frolov and Zelnikov, 2011). In the 1980s, Robinson and Carter (Krishnan, 2013) established the uniqueness theorems of the Kerr Newman solutions for the description of the black holes of nature This theorem states that; stationary axisymmetric solutions of Einstein’s equation for the vacuum, which have a smooth convex event horizon, are asymptotically flat and are non-singular outside of the horizon, are uniquely specified by the two parameters, the mass and the angular momentum and these two parameters only (Chandrasekhar, 1983). We apply Gauss’ divergence theorem to compute the fluxes of vector fields to support the claim that trapped and marginally trapped surfaces exist in the Kerr black hole This is the main result of this paper.
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