## On Point Mass Sources, Null Naked Singularities and Euclidean Gravitational Action as Entropy

**Authors:** Carlos Castro

It is rigorously shown how the static spherically symmetric solutions of Einstein's equations
can furnish a $null$ naked singularity associated with a point mass source at $ r = 0$.
The construction relies in the possibility of having a metric $discontinuity$ at the location of the point mass. This result should be contrasted with the spacelike singularity described by the textbook black hole solution. It has been argued by some authors why one cannot get any information from the null naked singularity so it will not have any undesirable physical effect to an outside far away observer and cannot cause a breakdown of predictability. In this way one may preserve the essence of the cosmic censorship hypothesis. The field equations due to a delta-function point-mass source at $ r = 0 $ are solved and the Euclidean gravitational action (in $ \hbar $ units) corresponding to those solutions
is evaluated explicitly. It is found that it is precisely equal to the black hole entropy (in Planck area units). This result holds in any dimensions $ D \ge 3 $. We finalize by arguing why the Noncommutative Gravity of the spacetime tangent (co-tangent) bundle is the proper arena to study point masses.

**Comments:** 14 Pages. Submitted to the Int. J. Mod. Phys. A

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### Submission history

[v1] 2012-01-23 06:30:16

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