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.
