TITLE:
A Novel Derivation of Black Hole Entropy in all Dimensions from Truly Point Mass Sources
AUTHORS:
Carlos Castro Perelman
KEYWORDS:
General Relativity, Black Holes, Entropy, Strings
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.10 No.3,
July
12,
2024
ABSTRACT: It is explicitly shown how the Schwarzschild Black Hole Entropy (in all dimensions) emerges from truly point mass sources at
r=0
due to a non-vanishing scalar curvature involving the Dirac delta distribution. In order to achieve this, one is required to extend the domain of r to negative values
−∞≤r≤+∞
. It is the density and anisotropic pressure components associated with the point mass delta function source at the origin
r=0
which furnish the Schwarzschild black hole entropy in all dimensions
D≥4
after evaluating the Euclidean Einstein-Hilbert action. Two of the most salient results are i) that the observed spacetime dimension
D=4
is precisely singled out from all the other dimensions when the strong and weak energy conditions are met, and ii) the point mass source described in this work is not the result of a spherically symmetric gravitational collapse of a star as described by the Oppenheimer-Snyder model because we are not neglecting the pressure. As usual, it is required to take the inverse Hawking temperature
β
H
as the length of the circle
S
β
1
obtained from a compactification of the Euclidean time in thermal field theory which results after a Wick rotation,
it=τ
, to imaginary time. This approach can be generalized to the Reissner-Nordstrom and Kerr-Newman metrics. The physical implications of this finding warrant further investigation since it suggests a profound connection between the notion of gravitational entropy and spacetime singularities.