Quantum power: a Lorentz invariant approach to Hawking radiation

Abstract

Particle radiation from black holes has an observed emission power depending on the surface gravity $\kappa = c^4/(4GM)$ as \begin{equation}\nonumber P_{\textrm{black hole}} \sim \frac{\hbar \kappa^2}{6\pi c^2} = \frac{\hbar c^6}{96\pi G^2 M^2}\,,\end{equation} while both the radiation from accelerating particles and moving mirrors (accelerating boundaries) obey similar relativistic Larmor powers, \begin{equation}\nonumber P_{\textrm{electron}}= \frac{q^2\alpha^2}{6\pi \epsilon_0 c^3}\,, \quad P_{\textrm{mirror}} =\frac{\hbar \alpha^2}{6\pi c^2}\,, \end{equation} where $\alpha$ is the Lorentz invariant proper acceleration. This equivalence between the Lorentz invariant powers suggests a close relation that could be used to understand black hole radiation. We show that an accelerating mirror with a prolonged metastable acceleration plateau can provide a unitary, thermal, energy-conserved analog model for black hole decay.