Comments on the non-existence of unified hoop conjecture

Abstract

In a recent article, Hod [1] has concluded the non-existence, heretofore unnoticed, of a unified Thorne's hoop conjecture that holds for the quasi-local mass, $\mathcal{M}(r\le R_{+})$ for static Reissner-Nordstrőm black hole, but does not hold for the spinning electrically charged Kerr-Newman black holes, when the same quasi-local mass is used. While the conclusion is correct and important, we wish to point out a curious exception for which the conjecture holds in a unified way for both the static and spinning \textit{tidal} charged $4d$ braneworld black holes of string theory, when the mass in the conjecture is the same quasi-local mass.

arXiv comment6 pages, 1 figure, 1 table

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