Could black hole thermodynamics play a role in black hole mergers?

TL;DR

This paper explores whether black hole thermodynamics, particularly the Davies phase transition point, can explain the observed clustering of black hole spins in gravitational wave data, by developing a thermodynamic fluctuation theory consistent with black hole physics.

Contribution

It constructs a thermodynamic fluctuation framework for Kerr black holes incorporating equilibrium conditions and accretion disk models, linking thermodynamics to merger dynamics.

Findings

The fluctuation theory aligns with Kerr thermodynamics.

Equilibrium conditions are consistent with accretion disk models.

Potential connection between thermodynamic phase transition and merger spin distribution.

Abstract

Gravitational waves from binary black hole mergers yield values for both the black hole remnant mass $M$ and it's spin $a$, with the $169$ $a$ values collected so far crowding significantly around their average $\bar{a}=0.6869\pm 0.087$. Could this crowding relate directly to the Davies phase transition point at $a=0.68125$ from black hole thermodynamics? I argue that a necessary challenge for such a connection requires a consistent application of the thermodynamic fluctuation theory that follows from black hole thermodynamics (BHT). Specifically, necessary are a correct choice of fluctuating variables, as well as thermal equilibrium between the event horizon at the Hawking temperature $\sim \mu K$ and the outside universe $\sim 3 K$. I show that the former requirement follows in straightforward fashion from the BHT of the Kerr model, while the later requires an accretion disk following the Novikov-Thorne accretion disk model. I construct a thermodynamic fluctuation theory meeting both these requirements. My results open the possibility that black hole mergers are based on some dynamical model (not known to me) with a limiting attractor state at the Davies point.