Tidal Love numbers and Green's functions in black hole spacetimes

TL;DR

This paper explores the relationship between tidal Love numbers and Green's functions in black hole spacetimes, emphasizing the role of radiation reaction effects and analyzing specific cases like BTZ black holes.

Contribution

It establishes a connection between Love numbers and Green's functions in dynamical black hole interactions, including the impact of radiation reaction effects.

Findings

Love numbers vanish for static asymptotically flat black holes in 4D GR

Green's functions fully describe dynamical response behavior

In BTZ black holes, absence of radiative modes simplifies the relation

Abstract

Tidal interactions play a crucial role in deciphering gravitational wave signals emitted by the coalescence of binary systems. They are usually quantified by a set of complex coefficients which include tidal Love numbers, describing the conservative response to an external perturbation. In the static case, these are found to vanish exactly for asymptotically flat black holes in general relativity in four spacetime dimensions, and recently they have been generalized to dynamical interactions. In the context of response theory, the retarded Green's function provides the complete description of the behavior of dynamical systems. In this work we investigate the relation between Love numbers and Green's functions, and highlight the relevance of radiation reaction effects to their connection. As a special case, we discuss Banados-Teitelboim-Zanelli black holes, where the absence of radiative modes allows us to make a direct link between them.