Dissipative Effects in the Worldline Approach to Black Hole Dynamics

TL;DR

The paper develops a long-wavelength, worldline EFT for Schwarzschild black holes that includes dissipative horizon dynamics by coupling localized worldline degrees of freedom to bulk fields. Absorption observables are fixed via matching to known horizon cross sections, enabling a universal description of horizon dissipation through two-point correlators of dipole and quadrupole operators. Electromagnetic and gravitational absorption are computed in various setups, including a charge in orbit and non-relativistic black hole binaries, with results expressed in terms of cross sections and correlators that can be applied to other compact objects. The framework provides a systematic, spin-agnostic path to incorporating horizon dissipation into gravitational-wave modeling and suggests connections to horizonduality ideas, while remaining anchored in EFT principles.

Abstract

We derive a long wavelength effective point particle description of four-dimensional Schwarzschild black holes. In this effective theory, absorptive effects are incorporated by introducing degrees of freedom localized on the worldline that mimic the interaction between the horizon and bulk fields. The correlation functions of composite operators in this worldline theory can be obtained by standard matching calculations. For example, we obtain the low frequency two-point function of multipole worldline operators by relating them to the long wavelength graviton black hole absorptive cross section. The effective theory is then used to predict the leading effects of absorption in several astrophysically motivated examples, including the dynamics of non-relativistic black hole binary inspirals and the motion of a small black hole in an arbitrary background geometry. Our results can be written compactly in terms of absorption cross sections, and can be easily applied to the dissipative dynamics of any compact object, e.g. neutron stars. The relation of our methodology to that developed in the context of the AdS/CFT correspondence is discussed.

Figures (2)

• Figure 1: Feynman diagram whose imaginary part gives the leading order contribution to the absorptive cross section. The dots correspond to insertions of leading multipole worldline operators.
• Figure 2: Leading order contribution to the absorptive potential. The dots correspond to insertions of the leading worldline multipole operators.