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

TL;DR

This work develops a unified framework to compute the dynamical tidal response of non-rotating black holes in GR by matching the horizon-ingoing MST solutions to a worldline EFT description of binary dynamics. It shows that the renormalized tidal response contains unavoidable scheme- and initial-condition ambiguities, yielding dynamical Love numbers that run logarithmically with scale due to UV divergences in the worldline EFT; after fixing the renormalization scheme (MS) and matching to MST, a finite, frequency-dependent dTLN emerges, vanishing in the static limit and contributing at 8PN to the waveform. The methodology integrates low-frequency BH perturbations with PN-inspired effective descriptions, enabling systematic inclusion of finite-size and dissipative effects in inspiral modeling. The results provide a principled path to extend to generic compact objects and to BHs in theories beyond GR, with potential observational relevance for future GW measurements where subleading tidal effects become detectable.

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.