Gravitational Radiation from a Particle Falling Radially into a Schwarzschild Black Hole

Abstract

We have computed the spectrum and energy of gravitational radiation from a "point test particle" of mass $m$ falling radially into a Schwarzschild black hole of mass $M\ensuremath{\gg}m$. The total energy radiated is about $0.0104m{c}^{2}(\frac{m}{M})$, 4 to 6 times larger than previous estimates; the energy is distributed among multipoles according to the empirical law ${E}_{2l\ensuremath{-}\mathrm{p}\mathrm{o}\mathrm{l}\mathrm{e}}\ensuremath{\approx}(\frac{0.44{m}^{2}{c}^{2}}{M}){e}^{\ensuremath{-}2l}$; and the total spectrum peaks at an angular frequency $\ensuremath{\omega}=\frac{0.32{c}^{3}}{\mathrm{GM}}$.