Dynamical Tidal Response of Schwarzschild Black Holes

TL;DR

This paper calculates the dynamical Love numbers of Schwarzschild black holes using an effective field theory approach, revealing finite contributions and matching classical solutions with quantum-inspired techniques.

Contribution

It introduces a method to compute finite scheme-dependent contributions to black hole Love numbers within an effective field theory framework.

Findings

Computed finite scheme-dependent Love number contributions.

Matched effective theory results with classical gravitational perturbations.

Extended understanding of black hole tidal responses in general relativity.

Abstract

Dynamical Love numbers capture the conservative response of an object to a time-dependent external tidal gravitational field. We compute the dynamical Love numbers of Schwarzschild black holes in general relativity within a point-particle effective field theory framework. In addition to the known logarithmic running, we compute the finite scheme-dependent contributions to the Love number couplings. We do this by matching the renormalized one-point function in the effective theory to the classical field profile computed in general relativity. On the general relativity side, we solve the Regge-Wheeler and Zerilli equations perturbatively in a small frequency expansion. In order to match on the effective field theory side we include gravitational interactions using the Born series and employ dimensional regularization to obtain a renormalized field profile.