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

TL;DR

This work identifies the low-frequency degrees of freedom of a black hole with near-horizon, non-compact gravitational perturbations organized as delocalized multipoles, whose dynamics are captured by a classical effective action in the CLEFT framework. It develops a horizon-boundary interaction description that couples near-horizon fields to asymptotic data and shows that the leading low-frequency scalar absorption cross section is universal, satisfying $sigma = A$, with a transmission amplitude $T = 2 i omega r0$, derived via matched asymptotic expansion and horizon-regular boundary conditions. The results provide a semiclassical, horizon-centric account of black-hole microstructure, suggesting that horizon degrees of freedom can be described without full quantum gravity and generalizing to other fields and spacetimes. Overall, the paper offers a concrete route to linking horizon physics with effective field theory concepts and sets the stage for exploring the microscopic origin of these horizon degrees of freedom.

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.