A generalization of Ryan's theorem: probing tidal coupling with gravitational waves from nearly circular, nearly equatorial, extreme-mass-ratio inspirals

TL;DR

This paper extends Ryan's theorem to show that gravitational waves from nearly circular, nearly equatorial EMRIs encode detailed information about the central body's spacetime, orbital evolution, and tidal interactions.

Contribution

It generalizes Ryan's theorem by including tidal coupling effects, demonstrating that gravitational waves encode more comprehensive information about the system.

Findings

Gravitational waves encode the central body's metric and orbital elements.

Tidal coupling effects can be inferred from gravitational wave data.

The theorem applies to nearly circular, nearly equatorial orbits.

Abstract

Extreme-mass-ratio inspirals (EMRIs) and intermediate-mass-ratio inspirals (IMRIs)--binaries in which a stellar-mass object spirals into a massive black hole or other massive, compact body--are important sources of gravitational waves for LISA and LIGO, respectively. Thorne has speculated that the waves from EMRIs and IMRIs encode, in principle, all the details of (i) the central body's spacetime geometry (metric), (ii) the tidal coupling (energy and angular momentum exchange) between the central body and orbiting object, and (iii) the evolving orbital elements. Fintan Ryan has given a first partial proof that this speculation is correct: Restricting himself to nearly circular, nearly equatorial orbits and ignoring tidal coupling, Ryan proved that the central body's metric is encoded in the waves. In this paper we generalize Ryan's theorem. Retaining Ryan's restriction to nearly circular and nearly equatorial orbits, and dropping the assumption of no tidal coupling, we prove that Thorne's conjecture is nearly fully correct: the waves encode not only the central body's metric but also the evolving orbital elements and (in a sense slightly different from Thorne's conjecture) the evolving tidal coupling.