Are Black Holes Springy?

Understand

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.