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. 

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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