Are Black Holes Springy?

TL;DR

This paper explores the analogy between black hole properties and spring mechanics, defining an effective spring constant related to black hole spin and temperature, and relating it to the maximum force conjecture in general relativity.

Contribution

It introduces a novel interpretation of black hole angular speed as a spring constant and connects it to surface gravity, temperature, and the maximum force conjecture.

Findings

Maximum spring constant equals Schwarzschild surface gravity.

Hawking temperature expressed in terms of the spring constant.

Force in extremal limit matches the maximum force conjecture.

Abstract

A $(3+1)$-dimensional asymptotically flat Kerr black hole angular speed $\Omega_+$ can be used to define an effective spring constant, $k=m\Omega_+^2$. Its maximum value is the Schwarzschild surface gravity, $k = \kappa $, which rapidly weakens as the black hole spins down and the temperature increases. The Hawking temperature is expressed in terms of the spring constant: $2\pi T = \kappa - k$. Hooke's law, in the extremal limit, provides the force $F = 1/4$, which is consistent with the conjecture of maximum force in general relativity.