Séminaire de Physique ThéoriqueExploring the symmetries of black hole: from perturbations to black hole mechanics
Jibril Ben Achour (ENS Lyon)
Thursday 23 November 2023 14:00 - Salle des séminaires - Salle 1180, bâtiment E2
Tidal deformation of compact objects are a powerful tool to infer their internal structure. They are encoded in the so called Love numbers which reflect the deformability of a given compact objects. In the case of four dimensional black holes solutions of General Relativity (GR), the Love numbers vanish. This property appears as a very special feature of 4d GR black holes as it is no longer true in higher dimensions nor in modified gravity theories. This has motivated a search for hidden symmetries which could explain this property, i.e. the Love symmetry.
In this talk, I will focus on one proposal called the HJPSS symmetry introduced in https://arxiv.org/abs/2105.01069 (and further discussed in https://arxiv.org/pdf/2212.09367.pdf) The origin of this symetry has remained unclear so far. In this talk, I will show that any static linear perturbations around Schwarzschild (and Kerr) black holes enjoy a symmetry under the Schrodinger group which explains the origin of the HJPSS structure. Then, I will show how this symmetry of static perturbations indeed forces the Love numbers to vanish for 4d Schwarzschild (and Kerr) black holes.
I will then connect this structure for static perturbations to known symmetry of black holes mechanics which appears in symmetry reduced GR. I will discuss the realization of these symmetries and comment on their relevance for the quantum mechanics of black holes.
This talk is based on the results presented in the following articles:
1) Symmetry of static black hole perturbations : https://arxiv.org/pdf/2202.12828.pdf
2) Symmetry and conformal bridge in Schwarzschild-(A)dS black hole mechanics: https://arxiv.org/pdf/2110.01455.pdf
3) Schrodinger-like symmetry of in black hole mechanics: https://arxiv.org/pdf/2302.07644.pdf