Hidden symmetry of the static response of black holes: applications to Love numbers
| Autor: | Achour, Jibril, Livine, Etera, Mukohyama, Shinji, Uzan, Jean-Philippe |
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| Přispěvatelé: | Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Institut d'Astrophysique de Paris (IAP), Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2022 |
| Předmět: |
High Energy Physics - Theory
Nuclear and High Energy Physics perturbation Galilei FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) algebra rotation General Relativity and Quantum Cosmology horizon conformal charge hidden symmetry black hole conservation law structure symmetry [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] diffeomorphism transformation spontaneous symmetry breaking Schwarzschild abelian High Energy Physics - Theory (hep-th) linear central charge [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc] mass entropy |
| Zdroj: | Journal of High Energy Physics |
| ISSN: | 1029-8479 |
| DOI: | 10.1007/jhep07(2022)112 |
| Popis: | We show that any static linear perturbations around Schwarzschild black holes enjoy a set of conserved charges which forms a centrally extended Schr\"{o}dinger algebra sh(1) = sl$(2,\mathbb{R}) \ltimes \mathcal{H}$. The central charge is given by the black hole mass, echoing results on black hole entropy from near-horizon diffeomorphism symmetry. The finite symmetry transformations generated by these conserved charges correspond to Galilean and conformal transformations of the static field and of the coordinates. This new structure allows one to discuss the static response of a Schwarzschild black hole in the test field approximation from a symmetry-based approach. First we show that the (horizontal) symmetry protecting the vanishing of the Love numbers recently exhibited by Hui et al, dubbed the HJPSS symmetry, coincides with one of the sl$(2,\mathbb{R})$ generators of the Schr\"{o}dinger group. Then, it is demonstrated that the HJPSS symmetry is selected thanks to the spontaneous breaking of the full Schr\"{o}dinger symmetry at the horizon down to a simple abelian sub-group. The latter can be understood as the symmetry protecting the regularity of the test field at the horizon. In the 4-dimensional case, this provides a symmetry protection for the vanishing of the Schwarzschild Love numbers. Our results trivially extend to the Kerr case. Comment: 22+5 pages, clarifications added on the symmetry criterion, extension to Kerr added in Appendix, version published in JHEP |
| Databáze: | OpenAIRE |
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