The Schwinger Mechanism, the Unruh Effect and the Production of Accelerated Black Holes

TL;DR

This paper explores the relationship between pair creation, the Unruh effect, and black hole thermodynamics, showing how quantum corrections and pair creation mechanisms underpin the thermal properties of accelerated systems and black holes.

Contribution

It establishes a direct link between pair creation amplitudes and the Unruh effect, demonstrating thermodynamical consistency and explaining black hole creation in thermal equilibrium.

Findings

Pair creation corrections relate to the Unruh effect.

The Euclidean action acts as an entropy in pair creation.

Black holes are created with Hawking temperature equal to Unruh temperature.

Abstract

We compute the corrections to the transition amplitudes of an accelerated Unruh ``box'' that arise when the accelerated box is replaced by a ``two level ion'' immersed in a constant electric field and treated in second quantization. There are two kinds of corrections, those due to recoil effects induced by the momentum transfers and those due to pair creation. Taken together, these corrections show that there is a direct relationship between pair creation amplitudes described by the Heisenberg-Euler-Schwinger mechanism and the Unruh effect, i.e. the thermalisation of accelerated systems at temperature $a/ 2 \pi$ where $a$ is the acceleration. In particular, there is a thermodynamical consistency between both effects whose origin is that the euclidean action governing pair creation rates acts as an entropy in delivering the Unruh temperature. Upon considering pair creation of charged black holes in an electric field, these relationships explain why black holes are created from vacuum in thermal equilibrium, i.e. with their Hawking temperature equal to their Unruh temperature.