Are Black Holes Springy?

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.

15 pages, 2 figures, fixed slow loading of Fig.2

References in corpus (6)

• The Kerr Metric
• The Kerr spacetime: A brief introduction
• Gravitational instability of an extreme Kerr black hole
• Black Holes, Information, and Hilbert Space for Quantum Gravity
• Maximum Tension: with and without a cosmological constant
• What are extremal Kerr Killing vectors up to?