Gravitational perturbations from NHEK to Kerr

TL;DR

This paper analyzes gravitational perturbations of near-extreme Kerr black holes, identifying modes responsible for deviations from extremality and exploring their implications for near-AdS2 holography.

Contribution

It provides a complete characterization of axisymmetric gravitational modes in near-NHEK geometry, including their effects on charges and reconstitution on Kerr.

Findings

Identified modes driving deviations from extremality.

Analyzed effects on Iyer-Wald charges.

Explored implications for nearly-AdS2 holography.

Abstract

We revisit the spectrum of linear axisymmetric gravitational perturbations of the (near-)extreme Kerr black hole. Our aim is to characterise those perturbations that are responsible for the deviations away from extremality, and to contrast them with the linearized perturbations treated in the Newman-Penrose formalism. For the near horizon region of the (near-)extreme Kerr solution, i.e. the (near-)NHEK background, we provide a complete characterisation of axisymmetric modes. This involves an infinite tower of propagating modes together with the much subtler low-lying mode sectors that contain the deformations driving the black hole away from extremality. Our analysis includes their effects on the line element, their contributions to Iyer-Wald charges around the NHEK geometry, and how to reconstitute them as gravitational perturbations on Kerr. We present in detail how regularity conditions along the angular variables modify the dynamical properties of the low-lying sector, and in particular their role in the new developments of nearly-AdS$_2$ holography.