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

Dimitrios Kosmopoulos, Davide Perrone, Mikhail Solon

TL;DR

The paper introduces Shell EFT, a gravity EFT that models a compact body as a spherical shell to regulate short-distance effects and to encode tidal responses via higher-dimensional operators. By marrying shell dynamics with known four-dimensional BH perturbation theory, it bypasses loop calculations and yields exact relations between shell Wilson coefficients and on-shell perturbations, enabling the computation of dynamical Love numbers for scalar perturbations through O(G^9) and agreement with prior BH results through O(G^7). A key result is the discovery of a Riemann zeta-function structure organizing the scheme-independent parts of the black-hole dynamical Love numbers, allowing an all-orders resummation and hinting at a link to quasi-normal modes. The framework provides a gauge-invariant, regulator-based route to dynamical tidal responses that can be extended to gravitons and Kerr black holes, with potential impact on gravitational-wave phenomenology and self-force calculations.

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.

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

TL;DR

The paper introduces Shell EFT, a gravity EFT that models a compact body as a spherical shell to regulate short-distance effects and to encode tidal responses via higher-dimensional operators. By marrying shell dynamics with known four-dimensional BH perturbation theory, it bypasses loop calculations and yields exact relations between shell Wilson coefficients and on-shell perturbations, enabling the computation of dynamical Love numbers for scalar perturbations through O(G^9) and agreement with prior BH results through O(G^7). A key result is the discovery of a Riemann zeta-function structure organizing the scheme-independent parts of the black-hole dynamical Love numbers, allowing an all-orders resummation and hinting at a link to quasi-normal modes. The framework provides a gauge-invariant, regulator-based route to dynamical tidal responses that can be extended to gravitons and Kerr black holes, with potential impact on gravitational-wave phenomenology and self-force calculations.

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 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.

Paper Structure

This paper contains 12 sections, 47 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Shell Effective Field Theory
  3. Dynamics in the Shell EFT
  4. Outside solution
  5. Inside solution
  6. Dynamics across the shell
  7. Love Numbers
  8. All-Orders Structure and Resummation
  9. Conclusions
  10. Acknowledgments
  11. From the Shell to the Worldline
  12. Results for Love numbers

Figures (1)

  • Figure 1: In the standard point-particle approach, calculating the tidal response involves loop contributions. By replacing the point particle with a shell, our EFT framework naturally incorporates known BHPT solutions in four-dimensions, thus bypassing the need for higher-order integration. Moreover, the matching to full theory is simplified since gravitational perturbations are described by the same solutions.