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arXiv · 2105.01069

Ladder Symmetries of Black Holes: Implications for Love Numbers and No-Hair Theorems

Lam Hui·Austin Joyce·Riccardo Penco·Luca Santoni·Adam R. Solomon
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Abstract

It is well known that asymptotically flat black holes in general relativity have a vanishing static, conservative tidal response. We show that this is a result of linearly realized symmetries governing static (spin 0,1,2) perturbations around black holes. The symmetries have a geometric origin: in the scalar case, they arise from the (E)AdS isometries of a dimensionally reduced black hole spacetime. Underlying the symmetries is a ladder structure which can be used to construct the full tower of solutions, and derive their general properties: (1) solutions that decay with radius spontaneously break the symmetries, and must diverge at the horizon; (2) solutions regular at the horizon respect the symmetries, and take the form of a finite polynomial that grows with radius. Taken together, these two properties imply that static response coefficients -- and in particular Love numbers -- vanish. Moreover, property (1) is consistent with the absence of black holes with linear (perturbative) hair. We also discuss the manifestation of these symmetries in the effective point particle description of a black hole, showing explicitly that for scalar probes the worldline couplings associated with a non-trivial tidal response and scalar hair must vanish in order for the symmetries to be preserved.

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Lam Hui, Austin Joyce, Riccardo Penco, Luca Santoni, Adam R. Solomon. 2021-05-03. Ladder Symmetries of Black Holes: Implications for Love Numbers and No-Hair Theorems. https://doi.org/10.1088/1475-7516%2F2022%2F01%2F032

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