Comments on "The Euclidean gravitational action as black hole entropy, singularities, and space-time voids" [J. Math. Phys. 49, 042501 (2008)]

We point out that the space-time 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 , in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962), Chap. 7, p. 227; also Phys. Rev. Lett. 4, 375 (1960). A. Mitra, Adv. Space Res. 38, 2917 (2006); Proceedings of the XIth Marcel-Grossmann Conference on General Relativity (World Scientific, Singapore, 2008), Vol. 3, p. 1968], 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 space-time void inferred by Castro is actually nonexistent.