A simple theoretical model for estimating the frequency characteristics of black hole mergers

Abstract

Gravitational waves, despite predicted within the Theory of General Relativity about a century ago, were observed experimentally only in the last few years, thanks to the recent advances of the LIGO and Virgo detectors. In this work, we introduce a simple theoretical model to study the gravitational irradiation of binary systems and derive the characteristics of the emitted gravitational waves (e.g., in terms of frequency). The simplicity of the model relies first on the consideration of the two-body problem and circular orbits. Second, we follow an energetic approach and make use of only one result of the Theory of General Relativity, to make the procedure clear and suitable for undergraduate education. The numerical solution is finally compared with the experimental data available for a few black hole mergers.