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 $$\kappa = c^4/(4GM)$$ κ = c 4 / ( 4 G M ) as $$\begin{aligned} P_{\text {black hole}} \sim \frac{\hbar \kappa ^2}{6\pi c^2} = \frac{\hbar c^6}{96\pi G^2 M^2}, \end{aligned}$$ P black hole ∼ ħ κ 2 6 π c 2 = ħ c 6 96 π G 2 M 2 , while both the radiation from accelerating particles and moving mirrors (accelerating boundaries) obey similar relativistic Larmor powers, $$\begin{aligned} P_{\text {electron}}= \frac{q^2\alpha ^2}{6\pi \epsilon _0 c^3}, \quad P_{\text {mirror}} =\frac{\hbar \alpha ^2}{6\pi c^2}, \end{aligned}$$ P electron = q 2 α 2 6 π ϵ 0 c 3 , P mirror = ħ α 2 6 π c 2 , where $$\alpha $$ 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.