Relativistic perturbation theory for black-hole boson clouds

Understand

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.