Quantum power: a Lorentz invariant approach to Hawking radiation

TL;DR

This paper proposes a Lorentz invariant framework linking black hole Hawking radiation to relativistic Larmor powers of accelerating particles and mirrors, using an analog model to explore black hole decay.

Contribution

It introduces a Lorentz invariant approach to black hole radiation, connecting it to accelerating boundary models and proposing an analog for black hole decay.

Findings

Accelerating mirrors with prolonged acceleration can model black hole decay.

Black hole radiation power relates to Lorentz invariant proper acceleration.

Analog models can provide insights into black hole thermodynamics.

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.