Abstract
We study the low-temperature limit of scalar perturbations of the Kerr-AdS5 black-hole for generic rotational parameters. We motivate the study by considering real-time holography of small black hole backgrounds. Using the isomonodromic technique, we show that corrections to the extremal limit can be encoded in the monodromy parameters of the Painlevé V transcendent, whose expansion is given in terms of irregular chiral conformal blocks. After discussing the contribution of the intermediate states to the quasinormal modes, we perform a numerical analysis of the low-lying frequencies. We find that the fundamental mode is perturbatively stable at low temperatures for small black holes and that excited perturbations are superradiant, as expected from thermodynamical considerations. We close by considering the holographic interpretation of the unstable modes and the decaying process.
Highlights
We show that corrections to the extremal limit can be encoded in the monodromy parameters of the Painlevé V transcendent, whose expansion is given in terms of irregular chiral conformal blocks
We reviewed the definition of asymptotic charges, discussed the geometrical meaning of the regularization involved in the definition of mass, and determined the holographic stress-energy tensor associated to the black hole in the dual field theory — whose thermal state is characterized by non-zero vacuum expectation values for all generators of the Weyl subgroup of the conformal group SO(4, 2)
We computed the first correction to the boundary-to-boundary scalar propagator due to the presence of the black hole and found that it makes scalar perturbations with dimension close to the marginal value (∆ = 4) irrelevant, suggesting that such perturbations should not substantially change the fate of the background as the theory flows to the IR
Summary
A1 and a2 are two independent rotation parameters. The mass relative to the AdS5 vacuum solution and the angular momenta were the subject of some discussion [34, 36,37,38]. To add to the confusion, we include our own derivation in appendix A. In the following it will be useful to redefine the black hole parameters in terms of the roots of ∆r. Which, for a regular, finite charged, dressed horizon black hole satisfy r02 < −1 < 0 < r−2 < r+2. Each non-zero root ri can be associated to a Killing horizon, only those of r− and r+ are physical. To each horizon we can associate the temperature Tk and angular velocities Ω1,k and Ω2,k, k = 0, +, −, given by. Where the prime stands for the derivative with respect to r. We note than T+ > 0, T− < 0 and T0 is purely imaginary
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