Relativistic perturbation theory for black-hole boson clouds

TL;DR

This paper develops a relativistic perturbation theory for scalar clouds around rotating black holes, improving accuracy over previous models and aiding gravitational-wave detection.

Contribution

It introduces a relativistic mode orthogonality and perturbation framework, surpassing non-relativistic approximations for black-hole boson clouds.

Findings

Close agreement with numerical relativity results

Accurate calculation of self-gravitational frequency shifts

Enhanced modeling for gravitational-wave astronomy

Abstract

We develop a relativistic perturbation theory for scalar clouds around rotating black holes. We first introduce a relativistic product and corresponding orthogonality relation between modes, extending a recent result for gravitational perturbations. We then derive the analog of time-dependent perturbation theory in quantum mechanics, and apply it to calculate self-gravitational frequency shifts. This approach supersedes the non-relativistic "gravitational atom" approximation, brings close agreement with numerical relativity, and has practical applications for gravitational-wave astronomy.