Abstract
The superradiant scattering of a scalar field with frequency and angular momentum (\omega,m) by a near-extreme Kerr black hole with mass and spin (M,J) was derived in the seventies by Starobinsky, Churilov, Press and Teukolsky. In this paper we show that for frequencies scaled to the superradiant bound the full functional dependence on (\omega,m,M,J) of the scattering amplitudes is precisely reproduced by a dual two-dimensional conformal field theory in which the black hole corresponds to a specific thermal state and the scalar field to a specific operator. This striking agreement corroborates a conjectured Kerr/CFT correspondence.
Highlights
A natural approach to this problem, continuing in the spirit of [2], is to try to generalize the near-horizon boundary conditions employed in [1] to allow non-chiral excitations.2 puzzles remain, this approach has recently met with partial success
We find that, up to a constant normalization prefactor, it is entirely reproduced from a hypothesis relating the excitations of extreme Kerr to those of a nonchiral CFT. (1.2) is exactly the CFT two point function of the CFT operator dual to the scalar field! This is our main result
Superradiance is a classical phenomenon in which an incident wave is reflected with an outgoing amplitude larger than the ingoing one, resulting in a negative absorption probability σabs < 0. This effect occurs for rotating black holes and allows energy to be extracted
Summary
Scattering by an extreme Kerr black hole involves infinitesimal excitations above extremality. The relevant limit is an adaptation to Kerr of a limit of Reissner-Nordstrom introduced in [12, 26].8 It is defined by taking TH → 0 and r → r+ while keeping the dimensionless near-horizon temperature. These coordinate transformations are singular on the boundary: the boundary regions where the far region is glued to the near region are not diffeomorphic for NHEK and near-NHEK. The Hawking temperature of the original black hole vanishes in this limit, observers at fixed r in near-NHEK measure a Hawking. In the limit we consider here, TR, nR and nR are held fixed while TH → 0 This means we are considering only those modes with energies very near the superradiant bound ω = mΩH. Modes with energies which do not scale to the bound have wavefunctions which do not penetrate into the near-NHEK region
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