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 . 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 . 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.
Living Rev. Relativity 15, (2012), 11
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