The Special Role of Toroidal Black Holes in Holography

Abstract

Grinberg and Maldacena have recently used certain thermal one-point functions, evaluated outside an AdS black hole, to determine the proper time of fall from the event horizon to the singularity (in the uncharged case) or to the Cauchy horizon (in the charged, unperturbed case). This raises the hope that one can use data outside the black hole to investigate the claim that black holes "have no interiors", by proving that the time of fall is exceptionally short, perhaps effectively zero. We examine this question for the particularly interesting case of a black hole (with a flat, toroidal event horizon) emitted by a larger black hole, after the manner postulated by the Weak Gravity Conjecture. We find that the proper time of fall to the Cauchy horizon is indeed always very short for these black holes, so they are prime candidates for an investigation of this kind.

On Black Hole Thermodynamics, Singularity, and Gravitational Entropy

“…In a recent work [85], Bousso and Shahbazi-Moghaddam even argued that "quantum singularities blurs the line between an ordinary singularities and a Cauchy horizon." Remarkably, whether spacetime continues to exist beyond a Cauchy horizon may be probed by the thermal one-point function of a massive field outside the black hole [86,87].…”