Gravitational radiation from hyperbolic orbits: comparison between self-force, post-Minkowskian, post-Newtonian, and numerical relativity results

TL;DR

This paper computes gravitational wave energy from hyperbolic orbits around a Schwarzschild black hole using a frequency-domain approach, comparing results with post-Minkowskian, post-Newtonian, self-force, and numerical relativity methods.

Contribution

It provides a detailed comparison of gravitational radiation calculations across multiple theoretical frameworks and numerical methods for hyperbolic orbits.

Findings

Agreement with post-Minkowskian results for large impact parameters and high velocities.

Validation of a simple PN-PM hybrid model for gravitational radiation.

First comparison of self-force and numerical relativity results for radiated energy.

Abstract

In this work I use a frequency-domain Regge-Wheeler-Zerilli approach to compute the gravitational wave energy radiated by a compact body moving along a hyperbolic or parabolic geodesic of a Schwarzschild black hole. I compare my results with the latest post-Minkowskian (PM) calculations for the radiated energy and find agreement for hyperbolic orbits with large impact parameters and characterized by a velocity at infinity, $v_\infty$, as large as $v_\infty/c=0.7$. I also find agreement between my results and the leading-order PM expansion for the radiation absorbed by the black hole. I make further comparisons with post-Newtonian (PN) theory and show the effectiveness of a simple PN-PM hybrid model. Finally, I make a first comparison of the radiated energy between self-force and numerical relativity.