Are Black Holes Springy?

A $(3+1)$-dimensional asymptotically flat Kerr black hole angular speed ${\mathrm{\Omega }}_{+}$ can be used to define an effective spring constant, $k=m{\mathrm{\Omega }}_{+}^2$. 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: $2\pi T = \kappa - k$\mathrm{.}Hook{e}^{\mathrm{\prime }}slaw,intheextremallimit,providestheforce$F = 1/4$, which is consistent with the conjecture of maximum force in general relativity.