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

TL;DR

The paper investigates whether the clustering of remnant BH spins near the Davies point $a^*=0.68125$ reflects a physical Davies phase transition from black hole thermodynamics. By formulating a thermodynamic fluctuation theory (TFT) for a Kerr BH and introducing a co-rotating, Novikov-Thorne disk–mediated environment to achieve horizon-level equilibrium, it argues that mass fluctuations $\{M\}$ are the relevant fluctuating degree of freedom and that $C_J$ diverges at $a^*$, consistent with a DP. Using observational data (168+ remnant spins with an average around $a^*$ and a skew ratio $sr\approx 0.58$) and a mass-fluctuation analysis showing $\sqrt{\langle(\\Delta m)^2\\rangle} \propto (a-a^*)^{-1/2}$ near $a^*$, the work presents a coherent TFT picture linking BH mergers to a potential attractor state at the Davies point. If validated, this framework could point toward a dynamical mechanism in BH mergers that bridges general relativity with quantum aspects of black hole thermodynamics, motivating further data collection and deeper theoretical modeling. All mathematical expressions are written with explicit $...$ delimiters as needed.

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 $\sim μK$ 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.

Figures (7)

• Figure 1: The observed post-merger data: (a) values of the remnant spins $a$ arranged in rough order of increasing time of observation, showing that $a$ tends to crowd around the Davies point at $a=a^*=0.68125$, pictured in dashed red, and (b) values of the remnant masses $m$ (in solar units $M_\odot$), which show no particular pattern.
• Figure 2: The heat capacity as a function of the spin $a=|J|/M^2$. $C_J$ diverges and changes sign at the Davies point $a=a^*=0.68125$, indicated with the dashed red line.
• Figure 3: Sketch of two basic structures framing thermodynamic fluctuation theory for black holes: (a) a spinning black hole surrounded by a non-spinning environment (the rest of the universe), and (b) a spinning black hole connected to the non-spinning environment via an intermediate spinning accretion disc. Fluctuations in the black hole are mediated via Hawking radiation Hawking1976 at the event horizon, indicated with a red circle. I start my discussion of the Davies point with scenario (a), and then argue that a correct picture must include the accretion disc in (b) in order to achieve thermal equilibrium at the event horizon.
• Figure 4: The spin $a$ as a function of the black hole mass $m$ (in units of $10^6$$M_\odot$) for supermassive black holes Reynolds2021. The blue dots have their upper error bars at $a<1$, and the red dots have their upper errors bars at $a=1$, with their data points placed at their lower error bars.
• Figure 5: The fluctuations $\sqrt{\langle(\Delta m)^2\rangle}$ (in solar mass units $M_\odot$) as a function of $(a-a^*)$. The exact and the asymptotic expressions are nearly identical.