Head-on collisions of black holes: the particle limit

TL;DR

This paper calculates gravitational waveforms and energies from a particle falling into a Schwarzschild black hole, revealing non-monotonic energy dependence on initial separation and unique spectral features.

Contribution

It provides a comprehensive catalog of waveforms and spectra for particle infall into black holes, including new insights into energy dependence and spectral structures.

Findings

Radiated energy peaks at initial radius ~4.5M.

Spectra for certain initial radii show evenly spaced bumps.

Comparison with approximation methods validates results.

Abstract

We compute gravitational radiation waveforms, spectra and energies for a point particle of mass $m_0$ falling from rest at radius $r_0$ into a Schwarzschild hole of mass $M$. This radiation is found to lowest order in $(m_0/M)$ with the use of a Laplace transform. In contrast with numerical relativity results for head-on collisions of equal-mass holes, the radiated energy is found not to be a monotonically increasing function of initial separation; there is a local radiated-energy maximum at $r_0\approx4.5M$. The present results, along with results for infall from infinity, provide a complete catalog of waveforms and spectra for particle infall. We give a representative sample from that catalog and an interesting observation: Unlike the simple spectra for other head-on collisions (either of particle and hole, or of equal mass holes) the spectra for $\infty>r_0>\sim5M$ show a series of evenly spaced bumps. A simple explanation is given for this. Lastly, our energy vs. $r_0$ results are compared with approximation methods used elsewhere, for small and for large initial separation.