Quantum power: a Lorentz invariant approach to Hawking radiation

Particle radiation from black holes has an observed emission power depending on the surface gravity $κ= c^4/(4GM)$ as \begin{equation}\nonumber P_{\textrm{black hole}} \sim \frac{\hbar κ^2}{6πc^2} = \frac{\hbar c^6}{96πG^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^2α^2}{6πε_0 c^3}\,, \quad P_{\textrm{mirror}} =\frac{\hbar α^2}{6πc^2}\,, \end{equation} where $α$ 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.

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