Regularity of a General Class of “Quantum Deformed” Black Holes

Abstract

We discuss the “quantum deformed Schwarzschild spacetime”, as originally introduced by Kazakov and Solodukhin in 1993, and investigate the precise sense in which it does and does not satisfy the desiderata for being a “regular black hole”. We shall carefully distinguish (i) regularity of the metric components, (ii) regularity of the Christoffel components, and (iii) regularity of the curvature. We shall then embed the Kazakov–Solodukhin spacetime in a more general framework where these notions are clearly and cleanly separated. Finally, we analyze aspects of the classical physics of these “quantum deformed Schwarzschild spacetimes”. We shall discuss the surface gravity, the classical energy conditions, null and timelike geodesics, and the appropriate variant of the Regge–Wheeler equation.

Geodesic congruences in modified Schwarzschild black holes

“…In this paper, we investigated two different kinds of modified Schwarzschild black holes, namely the Schwarzschild-Klinkhamer black hole [10] and the quantum deformed Schwarzschild black hole [8,9]. These two kinds of black holes could return to the standard Schwarzschild black hole by setting a vanishing regulator: b = 0 for the Schwarzschild-Klinkhamer black hole and a = 0 for the quantum deformed Schwarzschild black hole.…”

“…The QDS metric (32) returns to the standard Schwarzschild metric if a = 0. The original Schwarzschild singularity at r = 0 is now been "smeared out" to finite r [9]. Note that all components of the metric (32) are regular at r = a.…”

“…which is also divergent at r = a. This curvature singularity can be removed if one consider more general QDS black holes [9]. In Appendix C, we will briefly discuss this general class of QDS black holes and study their geodesic congruences.…”

“…Recently, the author of Ref. [9] proposed a generalized a e-mail: ziliang.wang@just.edu.cn (corresponding author) two-parameter class of QDS black holes which have better regularities.…”

Bounce corrections to gravitational lensing, quasinormal spectral stability and gray-body factors of Reissner-Nordström black holes

“…The research originates from a bounce parameter associated with the Plank scale introduced [16] by Visser et al in the modification of the Schwarzschild black hole. A great variety of solutions based on bounce and quantum corrections have been obtained [17][18][19][20][21], which provides us with the treatment for the singularities of black holes. All of these black hole mimickers are globally free from curvature singularities.…”