Empirical Energy Loss in Selected Binary Black Hole Mergers and Limitations of Mass-Ratio Scaling Models

Author: Efe Yenice

Abstract

We investigate the fraction of mass converted into gravitational wave energy during selected binary black hole mergers using published LIGO/Virgo parameter estimates. By analyzing representative events such as GW150914, GW151226, and GW190521, we obtain fractional mass-loss estimates of order 4%-6% of the total initial mass-energy.

We compare these estimates with a simplified mass-ratio-based scaling model, where the efficiency is assumed to depend only on the binary mass ratio. We find that this simplified scaling can underestimate the observed energy loss, illustrating the importance of strong-field general relativistic effects near merger, including nonlinear spacetime dynamics and ISCO physics.

Our results suggest an approximately common efficiency scale of order η≈0.05 among the selected events, while a larger analysis would be required to quantify dependence on mass ratio, spin, and other parameters. This provides a minimal empirical framework for a rough estimation of gravitational wave energy loss without full numerical relativity simulations.

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