Are Black Holes Springy?

A $(3+1)$-dimensional asymptotically flat Kerr black hole angular speed $Ω_+$ can be used to define an effective spring constant, $k=mΩ_+^2$. Its maximum value is the Schwarzschild surface gravity, $k = κ$, which rapidly weakens as the black hole spins down and the temperature increases. The Hawking temperature is expressed in terms of the spring constant: $2πT = κ- k$. 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.

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