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Novel Remarks on Point Mass Sources, Firewalls, Null Singularities and Gravitational Entropy

Abstract:

A continuous family of static spherically symmetric solutions of Einstein’s vacuum field equations with a spatial singularity at the origin $$ r = 0 $$r=0 is found. These solutions are parametrized by a real valued parameter $$ \lambda $$λ (ranging from 0 to 1) and such that the radial horizon’s location is displaced continuously towards the singularity ($$ r = 0 $$r=0) as $$ \lambda $$λ increases. In the extreme limit $$ \lambda = 1$$λ=1, the location of the singularity and horizon merges leading to a null singularity. In this extreme case, any infalling observer hits the null singularity at the very moment he/she crosses the horizon. This fact may have important consequences for the resolution of the fire wall problem and the complementarity controversy in black holes. An heuristic argument is provided how one might avoid the Hawking particle emission process in this extreme case when the singularity and horizon merges. The field equations due to a delta-function point-mass source at $$ r = 0 $$r=0 are solved and the Euclidean gravitational action corresponding to those solutions is evaluated explicitly. It is found that the Euclidean action is precisely equal to the black hole entropy (in Planck area units). This result holds in any dimensions $$ D \ge 3 $$D≥3.