Gravitational radiation from a particle plunging into a Schwarzschild black hole: frequency-domain and semirelativistic analyses

TL;DR

This paper improves the analysis of gravitational waves from particles plunging into Schwarzschild black holes by enhancing numerical methods and comparing frequency-domain and semirelativistic approaches, revealing universal late-time waveform behavior.

Contribution

It generalizes a transformation to improve source term decay, enhancing numerical convergence in gravitational wave calculations for unbound orbits.

Findings

Enhanced numerical convergence with the generalized transformation.

Recovered and expanded previous results on energy radiated.

Discovered universal late-time waveform behavior.

Abstract

We revisit the classic problem of gravitational wave emission by a test particle plunging into a Schwarzschild black hole both in the frequency-domain Regge-Wheeler-Zerilli formalism and in the semirelativistic approximation. We use, and generalize, a transformation due to Nakamura, Sasaki, and Shibata to improve the falloff of the source term of the Zerilli function. The faster decay improves the numerical convergence of quantities of interest, such as the energy radiated at spatial infinity through gravitational waves. As a test of the method, we study the gravitational radiation produced by test particles that plunge into the black hole with impact parameters close to the threshold for scattering. We recover and expand upon previous results that were obtained using the Sasaki-Nakamura equation. In particular, we study the relative contributions to the total energy radiated due to waves of axial and polar parity, and uncover an universal behavior in the waveforms at late times. We complement our study with a semirelativistic analysis of the problem, and we compare the two approaches. The generalized Nakamura-Sasaki-Shibata transformation presented here is a simple and practical alternative for the analysis of gravitational-wave emission by unbound orbits in the Schwarzschild spacetime using the frequency-domain Regge-Wheeler-Zerilli formalism.