Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory

TL;DR

This paper develops an effective field theory for compact bodies in gravity, capturing black hole perturbations and calculating scalar Love numbers to high order, revealing a zeta function structure in the results.

Contribution

It introduces a novel shell-based effective field theory that encodes gravitational perturbations directly from black hole solutions, simplifying complex calculations.

Findings

Derived scalar Love numbers up to order G^9 for Schwarzschild black holes.

Discovered a zeta function pattern in the scalar Love numbers.

Proposed a conjecture for the all-order structure of Love numbers.

Abstract

We construct a novel effective field theory for a compact body coupled to gravity, whose key feature is that the dynamics of gravitational perturbations is explicitly determined by known solutions in black hole perturbation theory in four dimensions. In this way, the physics of gravitational perturbations in curved space are already encoded in the effective field theory, thus bypassing the need for the higher-order calculations that constitute a major hurdle in standard approaches. Concretely, we model the compact body as a spherical shell, whose finite size regulates short-distance divergences in four dimensions and whose tidal responses are described by higher-dimensional operators. As an application, we consider scalar perturbations and derive new results for scalar Love numbers through ${\cal O} (G^9)$ for Schwarzschild black holes and for generic compact bodies. Finally, our analysis reveals an intriguing structure of the scalar black-hole Love numbers in terms of the Riemann zeta function, which we conjecture to hold to all orders.