Relativity and Cosmology


Exact Solutions of Einstein's Field Equations Associated to a Point-Mass Delta-Function Source

Authors: Carlos Castro

We explicitly solve the static spherically symmetric Einstein field equations due to a delta function point mass source at r = 0 and explain why our solutions are not diffeomorphic to the textbook solution. It is shown that the Euclidean action (in h-bar units) is precisely equal to the black hole entropy (in Planck area units). This result holds in any dimensions D >= 3 . Instead of a black-hole solution with a horizon at r = 2GM one has a spacetime void surrounding the singularity.

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Submission history

[v1] 9 Nov 2007

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