Infall of a particle into a black hole as a model for gravitational radiation from the galactic center

TL;DR

This paper models gravitational radiation from a particle falling into a Schwarzschild black hole, revealing spectral features and energy patterns, and discusses the detectability of such signals from the galactic center.

Contribution

It introduces a Laplace transform method to analyze gravitational radiation spectra from particle infall into black holes, highlighting spectral features and energy variations.

Findings

Spectra show evenly spaced bumps for initial radii between 5M and infinity.

Total radiated energy peaks around initial radius 4.5M.

Discusses potential detectability of galactic center black hole radiation.

Abstract

I present here the results of the study of the gravitational radiation generated by the infall (from rest at radius $r_0$) of a point particle of mass $m_0$ into a Schwarzschild black hole of mass $M$. We use Laplace's transform methods and find that the spectra of radiation for $\sim5M<r_0<\infty$ presents a series of evenly spaced bumps. The total radiated energy is not monotonically decreasing with $r_0$, but presents a joroba (hunch-back) at around $r_0\approx4.5M$. I finally discuss the detectability of the gravitational radiation coming from the black hole in the center of our galaxy.