Abstract It is well known that asymptotically flat black holes in generalrelativity have a vanishing static, conservative tidal response. We show that this is a result of linearly realized symmetries governingstatic (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 withradius spontaneously break the symmetries, and mustdiverge at the horizon;(2) solutions regular at the horizon respect the symmetries, andtake 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 probesthe 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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Ladder symmetries of black holes and de Sitter space: love numbers and quasinormal modes
In this note, we present a synopsis of geometric symmetries for (spin 0) perturbations around (4D) black holes and de Sitter space. For black holes, we focus on static perturbations, for which the (exact) geometric symmetries have the group structure of SO(1,3). The generators consist of three spatial rotations, and three conformal Killing vectors obeying a special
- Award ID(s):
- 2209997
- PAR ID:
- 10522830
- Publisher / Repository:
- Institute of Physics
- Date Published:
- Journal Name:
- Journal of Cosmology and Astroparticle Physics
- Volume:
- 2023
- Issue:
- 06
- ISSN:
- 1475-7516
- Page Range / eLocation ID:
- 056
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1475-7516/2023/06/056
