Charged black-bounce spacetimes

Abstract

Given the recent development of rotating black-bounce-Kerr spacetimes, for both theoretical and observational purposes it becomes interesting to see whether it might be possible to construct black-bounce variants of the entire Kerr-Newman family. Specifically, herein we shall consider black-bounce-Reissner-Nordström and black-bounce-Kerr-Newman spacetimes as particularly simple and clean everywhere-regular black hole “mimickers” that deviate from the Kerr-Newman family in a precisely controlled and minimal manner, and smoothly interpolate between regular black holes and traversable wormholes. While observationally the electric charges on astrophysical black holes are likely to be extremely low, |Q|/m ≪ 1, introducing any non-zero electric charge has a significant theoretical impact. In particular, we verify the existence of a Killing tensor (and associated Carter-like constant) but without the full Killing tower of principal tensor and Killing-Yano tensor, also we discuss how, assuming general relativity, the black-bounce-Kerr-Newman solution requires an interesting, non-trivial matter/energy content.

Killing Tensor and Carter Constant for Painlevé–Gullstrand Form of Lense–Thirring Spacetime

“…This tensor commutator also vanishes for Kerr-Newman spacetimes and for the black-bounce modifications of Kerr and Kerr-Newman spacetimes studied in [41,42]. Thus, the wave equation is separable on all of these spacetimes.…”

“…Similar oddities have also cropped up in other contexts. In references [41,42], those authors found that rotating black bounce spacetimes possess a nontrivial Killing tensor, and a 2-form square root thereof, but that this 2-form square root failed to be a Killing-Yano tensor.…”

Black-bounce to traversable wormhole

“…Theoretical physicists would then have experimentally informed clues as to which modifications to the Einstein equations are most desirable in working towards a so-called 'theory of everything' (or, indeed, whether an entirely different framework is required). Discussion regarding the extraction of astrophysical observables for nonsingular sample spacetimes in several frameworks can be found in references 4-17. One such family of candidate geometries which models alternatives to classical black holes is the family of 'black-bounce' spacetimes [18][19][20][21][22][23] . All of these black hole mimickers are globally free from curvature singularities, pass all weak-field observa-arXiv:2110.05657v2 [gr-qc] 20 Oct 2021 October 22, 2021 tional tests of standard GR, and belong either to the class of regular black holes or traversable wormholes.…”

Rotating spacetime: black-bounces and quantum deformed black hole

“…Recently, Jacopo Mazza, Edgardo Franzin and Stefano Liberati first generalized the Simpson-Visser (SV) spacetime to the Kerr case with Newman-Janis algorithm (NJA), and analyzed the properties of the exact solution [12]. Later in their work, they extended this situation to the Kerr-Newman spacetime [13].…”