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

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.

Published in J. Math. Phys. General Relativity Section

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