SciPost Phys. 8, 089 (2020) ·
published 17 June 2020
We study gravitational perturbations around the near horizon geometry of the
(near) extreme Kerr black hole. By considering a consistent truncation for the
metric fluctuations, we obtain a solution to the linearized Einstein equations.
The dynamics is governed by two master fields which, in the context of the
nAdS$_2$/nCFT$_1$ correspondence, are both irrelevant operators of conformal
dimension $\Delta=2$. These fields control the departure from extremality by
breaking the conformal symmetry of the near horizon region. One of the master
fields is tied to large diffeomorphisms of the near horizon, with its equations
of motion compatible with a Schwarzian effective action. The other field is
essential for a consistent description of the geometry away from the horizon.
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