The Delocalized Effective Degrees of Freedom of a Black Hole at Low Frequencies

TL;DR

This paper identifies the low-frequency degrees of freedom of black holes as delocalized near-horizon gravitational perturbations, clarifying their physical origin and analyzing their interactions and scattering properties.

Contribution

It explicitly connects near-horizon perturbations to effective degrees of freedom and derives their world-line action within the classical effective field theory framework.

Findings

Delocalized near-horizon perturbations are the fundamental low-frequency degrees of freedom.

The world-line action for these perturbations is derived within CLEFT.

The absorption cross section matches the horizon area for scalar wave scattering.

Abstract

Identifying the fundamental degrees of freedom of a black hole poses a long-standing puzzle. In hep-th/0511133 Goldberger and Rothstein forwarded a theory of the low frequency degrees of freedom within the effective field theory approach, where they are relevancy-ordered but of unclear physical origin. Here these degrees of freedom are identified with near-horizon but non-compact gravitational perturbations which are decomposed into delocalized multipoles. Their world-line (kinetic) action is determined within the classical effective field theory (CLEFT) approach and their interactions are discussed. The case of the long-wavelength scattering of a scalar wave off a Schwarzschild black hole is treated in some detail, interpreting within the CLEFT approach the equality of the leading absorption cross section with the horizon area.