Gravitational wave energy spectrum of hyperbolic encounters

TL;DR

This paper derives an analytical formula for the gravitational wave energy spectrum emitted during hyperbolic encounters of massive objects, confirming its accuracy against known limiting cases.

Contribution

It provides a new analytic expression for the gravitational wave energy spectrum in hyperbolic encounters, extending previous results to a broader range of eccentricities.

Findings

Analytic formula matches known parabolic and large eccentricity cases.

Numerical validation confirms the formula's accuracy.

Enhances understanding of gravitational wave emission in hyperbolic trajectories.

Abstract

The emission of gravitational waves is studied for a system of massive objects interacting on hyperbolic orbits within the quadrupole approximation following the work of Capozziello et al. Here we focus on the derivation of an analytic formula for the energy spectrum of the emitted waves. We checked numerically that our formula is in agreement with the two limiting cases for which results were already available: for the eccentricity {\epsilon} = 1, the parabolic case whose spectrum was computed by Berry and Gair, and the large {\epsilon} limit with the formula given by Turner.