# Symmetries of the Black Hole Interior and Singularity Regularization

### 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)

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

### Submission & Refereeing History

Resubmission 2010.07059v2 on 18 January 2021
Submission 2010.07059v1 on 15 October 2020

## Reports on this Submission

### 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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### Report

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

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -