Dissipative Effects in the Worldline Approach to Black Hole Dynamics

TL;DR

This paper develops an effective point particle theory for Schwarzschild black holes that incorporates dissipative effects like absorption, enabling predictions of black hole dynamics in astrophysical scenarios and relating to AdS/CFT methods.

Contribution

It introduces a novel worldline effective theory for black holes that models absorption effects via localized degrees of freedom, connecting gravitational absorption cross sections to worldline correlators.

Findings

Derived the low frequency two-point function of multipole operators.

Predicted absorption effects in black hole binary inspirals.

Applicable to dissipative dynamics of various compact objects.

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.