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Gravitational perturbations from NHEK to Kerr

Alejandra Castro Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090 GL Amsterdam, The Netherlands Victor Godet Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090 GL Amsterdam, The Netherlands; International Centre for Theoretical Sciences (ICTS-TIFR), Tata Institute of Fundamental Research, Shivakote, Hesaraghatta, Bangalore 560089, India Joan Simón School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom Wei Song Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China; Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China Boyang Yu Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China; Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China

arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2204.74003

2021.7
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.
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@inproceedings{alejandra2021gravitational,
  title={Gravitational perturbations from NHEK to Kerr},
  author={Alejandra Castro, Victor Godet, Joan Simón, Wei Song, and Boyang Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429150913672240164},
  year={2021},
}
Alejandra Castro, Victor Godet, Joan Simón, Wei Song, and Boyang Yu. Gravitational perturbations from NHEK to Kerr. 2021. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429150913672240164.
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