Gravitational perturbations from NHEK to Kerr

Alejandra Castro, Victor Godet, Joan Simon Soler, Wei Song, Boyang Yu

Research output: Contribution to journalArticlepeer-review

Abstract

We revisit the spectrum of linear 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-AdS2 holography.
Original languageEnglish
Number of pages73
JournalJournal of High Energy Physics
Publication statusAccepted/In press - 9 Jul 2021

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