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Symmetries of the Black Hole Interior and Singularity Regularization
by Marc Geiller, Etera R. Livine, Francesco Sartini
Submission summary
| Authors (as registered SciPost users): | Marc Geiller · Etera R. Livine · Francesco Sartini |
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| Preprint Link: | https://arxiv.org/abs/2010.07059v2 (pdf) |
| Date accepted: | Jan. 27, 2021 |
| Date submitted: | Jan. 18, 2021, 9:16 a.m. |
| Submitted by: | Marc Geiller |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
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| 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.
Author comments upon resubmission
Published as SciPost Phys. 10, 022 (2021)
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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.