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Symmetries of the Black Hole Interior and Singularity Regularization

by Marc Geiller, Etera R. Livine, Francesco Sartini

Submission summary

As Contributors: Marc Geiller
Arxiv Link: https://arxiv.org/abs/2010.07059v2 (pdf)
Date accepted: 2021-01-27
Date submitted: 2021-01-18 09:16
Submitted by: Geiller, Marc
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Gravitation, Cosmology and Astroparticle Physics
Approach: Theoretical

Abstract

We reveal an $\mathfrak{iso}(2,1)$ Poincar\'e algebra of conserved charges associated with the dynamics of the interior of black holes. The action of these Noether charges integrates to a symmetry of the gravitational system under the Poincar\'e group ISO$(2,1)$, which allows to describe the evolution of the geometry inside the black hole in terms of geodesics and horocycles of AdS${}_2$. At the Lagrangian level, this symmetry corresponds to M\"obius transformations of the proper time together with translations. Remarkably, this is a physical symmetry changing the state of the system, which also naturally forms a subgroup of the much larger $\textrm{BMS}_{3}=\textrm{Diff}(S^1)\ltimes\textrm{Vect}(S^1)$ group, where $S^1$ is the compactified time axis. It is intriguing to discover this structure for the black hole interior, and this hints at a fundamental role of BMS symmetry for black hole physics. The existence of this symmetry provides a powerful criterion to discriminate between different regularization and quantization schemes. Following loop quantum cosmology, we identify a regularized set of variables and Hamiltonian for the black hole interior, which allows to resolve the singularity in a black-to-white hole transition while preserving the Poincar\'e symmetry on phase space. This unravels new aspects of symmetry for black holes, and opens the way towards a rigorous group quantization of the interior.

Published as SciPost Phys. 10, 022 (2021)



Author comments upon resubmission

In this second version of the manuscript all the changed suggested by the referees have been implemented.

Reports on this Submission

Anonymous Report 2 on 2021-1-18 Invited Report

Report

The authors have addressed all of my suggestions and I am happy to recommend publication.

Requested changes

I have one optional suggestion for the authors: it might be helpful to add a reference to Appendix B below Eq. (2.7) for a more detailed explanation on why this choice for the lapse leads to a closed CVH algebra.

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Anonymous Report 1 on 2021-1-18 Invited Report

Report

The authors have satisfactorily addressed all my comments. Therefore, I am happy to recommend this interesting article for publication.

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