A Maximum Force Perspective on Black Hole Thermodynamics, Quantum Pressure, and Near-Extremality

TL;DR

This paper explores the concept of maximum force in black hole thermodynamics, linking it to near-extremality, quantum fluctuations, and horizon instability, offering new insights into black hole physics.

Contribution

It introduces a thermodynamic force perspective that characterizes near-extremality and incorporates quantum-induced pressure, connecting maximum force to horizon fluctuations.

Findings

Charge and angular momentum at maximum force relate to near-extremality.

Quantum fluctuations induce a pressure term in black hole thermodynamics.

Maximum force is associated with horizon instability and quantum phenomena.

Abstract

I re-examined the notion of the thermodynamic force constructed from the first law of black hole thermodynamics. In general relativity, the value of the charge (or angular momentum) at which the thermodynamic force equals the conjectured maximum force $F=1/4$ is found to correspond to $Q^2/M^2=8/9$ (respectively, $a^2/M^2=8/9$), which is known in the literature to exhibit some special properties. This provides a possible characterization of near-extremality. In addition, taking the maximum force conjecture seriously amounts to introducing a pressure term in the first law of black hole thermodynamics. This resolves the factor of two problem between the proposed maximum value $F=1/4$ and the thermodynamic force of Schwarzschild spacetime $F=1/2$. Surprisingly it also provides another indication for the instability of the inner horizon. For a Schwarzschild black hole, under some reasonable assumptions, this pressure can be interpreted as being induced by the quantum fluctuation of the horizon position, effectively giving rise to a diffused "shell" of characteristic width $\sqrt{M}$. The maximum force can therefore, in some contexts, be associated with inherently quantum phenomena. Some implications are discussed as more questions are raised.