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General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th
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.
