Effective field theory of black hole echoes

Abstract

Gravitational wave 'echoes' during black-hole merging events have been advocated as possible signals of modifications to gravity in the strong-field (but semiclassical) regime. In these proposals the observable effect comes entirely from the appearance of nonzero reflection probability at the horizon, which vanishes for a standard black hole. We show how to apply EFT reasoning to these arguments, using and extending earlier work for localized systems that relates choices of boundary condition to the action for the physics responsible for these boundary conditions. EFT reasoning applied to this action argues that linear 'Robin' boundary conditions dominate at low energies, and we determine the relationship between the corresponding effective coupling (whose value is the one relevant low-energy prediction of particular modifications to General Relativity for these systems) and the phenomenologically measurable near-horizon reflection coefficient. Because this connection involves only near-horizon physics it is comparatively simple to establish, and we do so for perturbations in both the Schwarzschild geometry (which is the one most often studied theoretically) and the Kerr geometry (which is the one of observational interest for post-merger ring down). In passing we identify the renormalization-group evolution of the effective couplings as a function of a regularization distance from the horizon, that enforces how physics does not depend on the precise position where the boundary conditions are imposed. We show that the perfect-absorber/perfectemitter boundary conditions of General Relativity correspond to the only fixed points of this evolution. Nontrivial running of all other RG evolution reflects how modifications to gravity necessarily introduce new physics near the horizon. arXiv:1808.00847v2 [gr-qc]

Analytical model for gravitational-wave echoes from spinning remnants

“…In a follow-up paper we plan to adopt the template developed here in a matched-filtered search for GW echoes using LIGO/Virgo public data and for a Bayesian parameter estimation. This can be done for a generic reflectivity coefficient R, or for specific models, such as those motivated by effective field the-ory arguments [80] and the model recently proposed in Refs. [4,68] for the Boltzmann reflectivity of quantum BHs.…”

Phenomenological aspects of black holes beyond general relativity

“…Due to the existence of this maximum in the potential, outgoing waves originated at r < r ph will be backscattered. The fraction of backscattered radiation can be calculated explicitly [185][186][187][188]. Only objects that are compact enough to have a photon sphere will display this phenomenon, and therefore we focus in the following on these objects.…”

A WKB formula for echoes

“…This has been recently considered in Ref. [11,12,38,50,51]). It should be stressed that this is true only when the background spacetime in the exterior of the ultra compact object is the Kerr spacetime.…”