Gravitational radiation from collisions at the speed of light: a massless particle falling into a Schwarzschild black hole

TL;DR

This paper analyzes gravitational waves emitted when a massless particle falls into a Schwarzschild black hole, revealing that less than half of the energy radiates as quadrupole waves, with a flat spectrum and agreement with theoretical predictions.

Contribution

It provides a fully relativistic calculation of gravitational radiation from a massless particle infall, extending understanding of high-speed black hole collisions.

Findings

Less than 50% of energy radiated as quadrupole waves

Spectra is flat across frequencies

Zero frequency limit matches Smarr's prediction

Abstract

We compute spectra, waveforms, angular distribution and total gravitational energy of the gravitiational radiation emitted during the radial infall of a massless particle into a Schwarzschild black hole. Our fully relativistic approach shows that (i) less than 50% of the total energy radiated to infinity is carried by quadrupole waves, (ii) the spectra is flat, and (iii) the zero frequency limit agrees extremely well with a prediction by Smarr. This process may be looked at as the limiting case of collisions between massive particles traveling at nearly the speed of light, by identifying the energy $E$ of the massless particle with $m_0 \gamma$, $m_0$ being the mass of the test particle and $\gamma$ the Lorentz boost parameter. We comment on the implications for the two black hole collision at nearly the speed of light process, where we obtain a 13.3% wave generation efficiency, and compare our results with previous results by D'Eath and Payne.