Dynamical Tidal Response of Non-rotating Black Holes: Connecting the MST Formalism and Worldline EFT

TL;DR

This paper connects the MST formalism and worldline EFT to analyze the dynamical tidal response of non-rotating black holes in GR, revealing scheme-dependent tidal Love numbers and discussing extensions beyond GR.

Contribution

It introduces a unified analytical framework combining MST and EFT methods to compute black hole tidal responses, highlighting scheme ambiguities and potential extensions.

Findings

Renormalized tidal response functions have scheme-dependent ambiguities.

Fixed ambiguities yield dynamical tidal Love numbers.

Framework applicable to non-rotating compact objects and beyond-GR theories.

Abstract

The response of a black hole (BH) to tidal forces encodes key information about the underlying gravitational theory and affects the waveform of gravitational waves emitted during binary inspiral processes. In this paper, we analyze the dynamical tidal response of static and spherically symmetric BHs in a low-frequency regime within general relativity (GR), based on a matching between the Mano-Suzuki-Takasugi (MST) methods for an analytical approach to BH perturbations and the worldline effective field theory (EFT) for an efficient and unified computation of the binary dynamics within the post-Newtonian regime. We show that the renormalized tidal response function is subject to inevitable ambiguities associated with the choice of renormalization scheme and with the initial condition of the renormalization flow equation. Once these ambiguities are fixed, we obtain scheme-dependent dynamical tidal Love numbers. We also discuss possible extensions of our formalism, including generic non-rotating compact objects (e.g., neutron stars) in GR and BHs in theories beyond GR.