http://arxiv.org/abs/2105.01069
It is well known that asymptotically flat black holes in general relativity have a vanishing static tidal response and no static hair. We show that both are 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. Property (1) implies no hair; (1) and (2) combined imply that static response coefficients — and in particular Love numbers — vanish. 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.
L. Hui, A. Joyce, R. Penco, et. al.
Tue, 1 Jun 21
24/72
Comments: N/A