Semi-relativistic approximation to gravitational radiation from encounters with nonspinning black holes

TL;DR

This paper introduces a semirelativistic method to accurately estimate gravitational wave energy and angular momentum loss during close encounters with nonspinning black holes, improving previous models and aligning with detailed simulations.

Contribution

It develops a semirelativistic approximation for gravitational radiation from high-eccentricity orbits near black holes, enhancing accuracy over Newtonian models and matching Teukolsky-based results.

Findings

Improved flux formulas for energy and angular momentum loss.

Good agreement with Teukolsky simulations for low eccentricity orbits.

Enhanced modeling for gravitational wave capture rate estimates.

Abstract

The capture of compact bodies by black holes in galactic nuclei is an important prospective source for low frequency gravitational wave detectors, such as the planned Laser Interferometer Space Antenna. This paper calculates, using a semirelativistic approximation, the total energy and angular momentum lost to gravitational radiation by compact bodies on very high eccentricity orbits passing close to a supermassive, nonspinning black hole; these quantities determine the characteristics of the orbital evolution necessary to estimate the capture rate. The semirelativistic approximation improves upon treatments which use orbits at Newtonian-order and quadrupolar radiation emission, and matches well onto accurate Teukolsky simulations for low eccentricity orbits. Formulae are presented for the semirelativistic energy and angular momentum fluxes as a function of general orbital parameters.