A Maximum Entropy Conjecture for Black Hole Mergers

TL;DR

This paper proposes a thermodynamic principle, based on entropy maximization, that may govern the final state of black hole mergers, showing close agreement with numerical relativity predictions.

Contribution

It introduces an entropy maximization conjecture for black hole mergers using post-Newtonian and numerical relativity data, suggesting thermodynamics influences the final black hole state.

Findings

Entropy peaks near the final remnant parameters.

Agreement within a few percent with numerical relativity results.

Supports a thermodynamic principle in black hole mergers.

Abstract

The final state of a binary black hole merger is predicted with high precision by numerical relativity, but could there be a simple thermodynamic principle within general relativity that governs the selection of the remnant? Using post-Newtonian relations between the mass M (including the binding energy) and angular momentum J of quasi-circular, nonspinning binaries, we uncover a puzzling result: When the binary's instantaneous M and J are mapped to those of a hypothetical Kerr black hole, the corresponding entropy exhibits a maximum during the evolution. This maximum occurs at values of M and J strikingly close to those of the final remnant predicted by numerical relativity. Consistent behavior is observed when using the relation between M and J obtained from numerical relativity evolution. Although this procedure is somewhat ad hoc, the agreement between the masses and spins of the final state obtained from numerical relativity and the results of this maximum entropy procedure is remarkable, with agreement to within a few percent when using either post-Newtonian or numerical relativity results for M and J. These findings allow us to propose an entropy maximization conjecture for binary black hole mergers, hinting that thermodynamic principles may govern the selection of the final black hole state.