In Section 4, we presented how the entropy of any extremal black hole can be reproduced microscopically from one chiral half of one (or several) two-dimensional CFT(s). In this section, we will present arguments supporting the conjecture that this duality can be extended to near-extremal black holes dual to a CFT with a second sector slightly excited, following [53, 106, 160]. We will show that the derivation of [53, 106, 160] is supporting evidence for all CFTs presented in Section 4, as noted in [79, 71]. In the case of the dual to near-extremal spinning black holes, one can think intuitively that the second CFT sector is excited for the following reason: lights cones do not quite coalesce at the horizon, so microscopic degrees of freedom do not rotate at the speed of light along the single axial direction. The intuition for the other CFTs (, ) is less immediate.

Near-extremal black holes are defined as black holes with a Hawking temperature that is very small compared with their inverse mass

At finite energy away from extremality, one cannot isolate a decoupled near-extremal near-horizon geometry. As we discussed in Section 4, the extremal near-horizon geometry then suffers from infrared divergences, which destabilize the near-horizon geometry. This prevents one to formulate boundary conditions à la Brown-Henneaux to describe non-chiral excitations. Therefore, another approach is needed.If near-extremal black holes are described by a dual field theory, it means that all properties of these black holes – classical or quantum – can be derived from a computation in the dual theory, after it has been properly coupled to the surrounding spacetime. We now turn our attention to the study of one of the simplest dynamical processes around black holes: the scattering of a probe field. This route was originally followed for static extremal black holes in [208, 209]. In this approach, no explicit metric boundary conditions are needed. Moreover, since gravitational backreaction is a higher-order effect, it can be neglected. One simply computes the black-hole–scattering amplitudes on the black-hole background. In order to test the near-extremal black hole/CFT correspondence, one then has to determine whether or not the black hole reacts like a two-dimensional CFT to external perturbations originating from the asymptotic region far from the black hole.

We will only consider fields that probe the near-horizon region of near-extremal black holes. These probe fields have energy and angular momentum close to the superradiant bound ,

In order to simplify the notation, in this section we will drop all hats on quantities defined in the asymptotic region far from the black hole.Since no general scattering theory around near-extremal black-hole solutions of (1) has been proposed so far, we will concentrate our discussion on near-extremal asymptotically-flat Kerr–Newman black holes, as discussed in [53, 160] (see also [79, 72, 81, 74, 77, 3]). Extensions to the Kerr–Newman–AdS black hole or other specific black holes in four and higher dimensions in gauged or ungauged supergravity can be found in [53, 106, 73, 242, 46] (see also [71, 80, 129, 224]).

5.1 Near-extremal Kerr–Newman black holes

5.2 Macroscopic greybody factors

5.3 Macroscopic greybody factors close to extremality

5.4 Microscopic greybody factors

5.5 Microscopic accounting of superradiance

5.2 Macroscopic greybody factors

5.3 Macroscopic greybody factors close to extremality

5.4 Microscopic greybody factors

5.5 Microscopic accounting of superradiance

Living Rev. Relativity 15, (2012), 11
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