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Extreme-mass-ratio inspirals (EMRIs) and intermediate-mass-ratio inspirals(IMRIs)--binaries in which a stellar-mass object spirals into a massive blackhole or other massive, compact body--are important sources of gravitationalwaves for LISA and LIGO, respectively. Thorne has speculated that the wavesfrom EMRIs and IMRIs encode, in principle, all the details of (i) the centralbody's spacetime geometry (metric), (ii) the tidal coupling (energy and angularmomentum exchange) between the central body and orbiting object, and (iii) theevolving orbital elements. Fintan Ryan has given a first partial proof thatthis speculation is correct: Restricting himself to nearly circular, nearlyequatorial orbits and ignoring tidal coupling, Ryan proved that the centralbody's metric is encoded in the waves. In this paper we generalize Ryan'stheorem. Retaining Ryan's restriction to nearly circular and nearly equatorialorbits, and dropping the assumption of no tidal coupling, we prove thatThorne's conjecture is nearly fully correct: the waves encode not only thecentral body's metric but also the evolving orbital elements and (in a senseslightly different from Thorne's conjecture) the evolving tidal coupling.Comment: 10 pages, 1 figure, submitted to Phys. Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Generalization of Ryan’s theorem: Probing tidal coupling with gravitational waves from nearly circular, nearly equatorial, extreme-mass-ratio inspirals