Comments on "The Euclidean gravitational action as black hole entropy, singularities, and spacetime voids" by C. Castro, J. Math. Phys., 49, 042501, 2008

TL;DR

This paper critiques Castro's 2008 work by showing that the inferred spacetime void results from a gauge choice and that true Schwarzschild black holes have zero mass, rendering the void non-existent.

Contribution

It clarifies that the spacetime void in Castro's analysis is due to gauge choice and establishes that physical Schwarzschild black holes have zero gravitational mass.

Findings

Castro's spacetime void is due to a discontinuous gauge choice.

True Schwarzschild black holes have zero gravitational mass.

The supposed void is non-existent in physical solutions.

Abstract

We point out that the {\em spacetime void} inferred by Castro[J. Math. Phys. 49, 042501, (2008)] results from his choice of a discontinuous radial gauge. Further since the integration constant $\alpha_0 = 2M_0$ ($G=c=1$) occurring in the vacuum Hilbert/Schwarzschild solution of a neutral "point mass" is zero [Arnowitt et al., in Gravitation: An Introduction to Current Research, ed. L. Witten, Wiley, Chap. 7, p.227; also Phys. Rev. Lett., 4, 375, (1960)]; A. Mitra, Adv. Sp. Res., 38, 2917 (2006)] Castro's gauge reduces to the well behaved and physical Hilbert gauge. Physically this means that true Hilbert/Schwarzschild black holes have unique gravitational mass M=0. Accordingly, the unphysical {\em spacetime viod} inferred by Castro is actually non-existent.