Geodesic deviations: modeling extreme mass-ratio systems and their gravitational waves

TL;DR

This paper develops an analytic method using geodesic deviations to model gravitational waves from extreme mass-ratio systems in Schwarzschild space-time, providing accurate waveforms and energy emission estimates.

Contribution

It introduces an analytic approximation approach for geodesics and gravitational wave source terms in Schwarzschild space-time, improving understanding of wave emission in extreme mass-ratio binaries.

Findings

Analytic expressions for source terms in wave equations

Numerical solutions for gravitational waveforms at large distances

Computed gravitational wave power consistent with numerical methods

Abstract

The method of geodesic deviations has been applied to derive accurate analytic approximations to geodesics in Schwarzschild space-time. The results are used to construct analytic expressions for the source terms in the Regge-Wheeler and Zerilli-Moncrief equations, which describe the propagation of gravitational waves emitted by a compact massive object moving in the Schwarzschild background space-time. The wave equations are solved numerically to provide the asymptotic form of the wave at large distances for a series of non-circular bound orbits with periastron distances up to the ISCO radius, and the power emitted in gravitational waves by the extreme-mass ratio binary system is computed. The results compare well with those of purely numerical approaches.