Warped symmetries of the Kerr black hole
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Springer
Received: October 16, 2019 Accepted: November 30, 2019 Published: January 7, 2020
Ankit Aggarwal,a,b Alejandra Castrob and St´ ephane Detournaya a
Physique Mathematique des Interactions Fondamentales, Universite Libre de Bruxelles, Campus Plaine — CP 231, 1050 Bruxelles, Belgium b Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
E-mail: [email protected], [email protected], [email protected] Abstract: We propose a set of diffeomorphism that act non-trivially near the horizon of the Kerr black hole. We follow the recent developments of Haco-Hawking-Perry-Strominger to quantify this phase space, with the most substantial difference being our choice of vectors fields. Our gravitational charges are organized into a Virasoro-Kac-Moody algebra with non-trivial central extensions. We interpret this algebra as arising from a warped conformal field theory. Using the data we can infer from this warped CFT description, we capture the thermodynamic properties of the Kerr black hole. Keywords: AdS-CFT Correspondence, Black Holes, Conformal Field Theory, SpaceTime Symmetries ArXiv ePrint: 1909.03137
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)016
JHEP01(2020)016
Warped symmetries of the Kerr black hole
Contents 1
2 Black hole monodromy
3
3 Warped symmetries in the Kerr geometry 3.1 Central extensions
6 7
4 Black hole thermodynamics from warped symmetries
9
5 Discussion
11
A Aspects of warped conformal symmetries A.1 Modular transformations and canonical entropy
13 14
B Cardy growth revisited
15
C Hidden warped symmetries of the Klein-Gordon operator
16
1
Introduction
One remarkable success of the holographic principle is the link it provides between two dimensional conformal field theories, CFT2 , and the microscopic origin of black hole thermodynamics. This first connection was observed in the seminal derivation of the microscopic entropy of five-dimensional extremal BPS black holes in the context of string theory by Strominger and Vafa [1]. Despite the specificity of the construction, it provided a framework to explore the robustness of the result beyond its initial scope. Within supersymmetric theories the agreement has been outstanding, allowing for an exploration of both perturbative and non-perturbative effects in quantum gravity; see [2] for a review on the subject.1 Soon after this success, it became clear that the key feature was not supersymmetry, or the specific string theory ingredients in [1], but rather the conformal symmetry in the near horizon region. Conformal invariance is implied by the presence of an AdS factor in the near horizon region, and hence AdS/CFT is responsible for the agreement. For example, many of the above supersymmetric solutions contain an AdS3 factor, and it was soon evident that part of the above success relied on AdS3 /CFT2 . Among other properties, the entropy of these black holes agrees p
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