Independent of these constructions, the scattering probabilities of probes around the near-extremal Kerr–Newman black hole can be reproduced near the superradiant bound by manipulating near-chiral thermal two-point functions of a two-dimensional CFT. The result extends straightforwardly to other asymptotically-flat or AdS black holes in various gravity theories. Finally away from extremality, hidden symmetries are present in some scalar probes around the Kerr–Newman black hole close enough to the horizon. We showed that several CFTs are required to account for the entire probe dynamics in the near region in the regime of small mass, small energy and small charge. This analysis does not extend straightforwardly to AdS black holes.
These results – obtained in gravity coupled to matter – are naturally accounted for by assuming that the microstates of asymptotically-flat black holes, at extremality and away from extremality, can be described by CFTs and that the microstates of asymptotically-AdS black holes at extremality can be described by chiral halves of CFTs. Scattering amplitudes and hidden symmetries are also accounted for by assuming that part of the dynamics of black holes can be mapped to the dynamics of these CFTs once they are suitably coupled to the exterior black-hole region. By consistency with the gravitational analysis, several CFT descriptions are available when several compact symmetries are present. The existence of such CFTs is conjectural and only future research will tell how far these Kerr/CFT correspondences and their extensions can be made more precise.
A fair concluding remark would be that our understanding of the Kerr, Reissner–Nordström and Kerr–Newman black hole has increased over the last four years, but there is still a long road ahead of us to comprehend what these CFTs really are and what they are telling us about the nature of quantum black holes.
Living Rev. Relativity 15, (2012), 11
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