Gravitational Polarizability of Schwarzschild Black Holes

TL;DR

This paper investigates how Schwarzschild black holes respond to external quadrupolar perturbations, revealing their gravitational polarizability and its dependence on boundary conditions through a combination of classical and effective field theory methods.

Contribution

It provides a novel combined analysis using Regge-Wheeler equations and worldline effective field theory to describe black hole gravitational polarizability and its causality-related dispersion relations.

Findings

Classical 2-point correlation functions depend on boundary conditions.

Derived dispersion relations linking fluctuation and dissipation.

Consistent description combining classical and effective field theory approaches.

Abstract

The linear response of a Schwarzschild black hole to an external quadrupolar perturbation is studied in analogy to a mechanical electrodynamical system, with the goal to describe the gravitational polarizability. Its causality properties imply dispersion relations that relate fluctuation and dissipative properties. We review and combine results obtained via the Regge-Wheeler equation on one side and a perturbative, worldline effective field theory description on the other, obtaining a consistent description of the dispersion relations for the gravitational polarizability of a Schwarzschild black hole. We find that the classical part of the 2-point correlation function of the black hole multipole depends on the boundary conditions of the space-time the black hole is immersed in, which is relevant for the dispersion relations considered.