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
,
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
]).
http://www.livingreviews.org/lrr-2012-11 |
Living Rev. Relativity 15, (2012), 11
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