The radial equation has a more involved form than the corresponding flat equation (199) due to the fact
that
is a quartic instead of a quadratic polynomial in
; see (42
). More precisely, the quartic
polynomial
can be written as
It has been suggested that all these poles have a role to play in the microscopic description of the AdS
black hole [102]. It is an open problem to unravel the structure of the hidden symmetries,
if any, of the full non-extremal radial equation (203
). It has been shown that in the context
of five-dimensional black holes, one can find hidden conformal symmetry in the near-horizon
region close to extremality [46]. It is expected that one could similarly neglect the two complex
poles in the near-horizon region of near-extremal black holes, but this remains to be checked in
detail.17
Since much remains to be understood, we will not discuss AdS black holes further.
http://www.livingreviews.org/lrr-2012-11 |
Living Rev. Relativity 15, (2012), 11
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