Ladder symmetries of black holes. Implications for love numbers and no-hair theorems

Hui, Lam; Joyce, Austin; Penco, Riccardo; Santoni, Luca; Solomon, Adam R.

doi:10.1088/1475-7516/2022/01/032

Title: Ladder symmetries of black holes. Implications for love numbers and no-hair theorems

Journal Article · Tue Jan 18 00:00:00 EST 2022 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2022/01/032· OSTI ID:1979351

Hui, Lam ^[1]; Joyce, Austin ^[2]; Penco, Riccardo ^[3]; Santoni, Luca ^[1]; Solomon, Adam R. ^[3]

Columbia University, New York, NY (United States)
University of Amsterdam (Netherlands)
Carnegie Mellon University, Pittsburgh, PA (United States)

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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Research Organization:: Univ. of Arizona, Tucson, AZ (United States); Columbia Univ., New York, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); Simons Fellowship; National Science Foundation (NSF); Carnegie Mellon University

Grant/Contract Number:: FG02-04ER41338; FG02-06ER41449; SC0011941; PHY-1915611; 555117

OSTI ID:: 1979351

Journal Information:: Journal of Cosmology and Astroparticle Physics, Vol. 2022, Issue 01; ISSN 1475-7516

Publisher:: Institute of Physics (IOP)Copyright Statement

Country of Publication:: United States

Language:: English

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