Quantum Radiation of Uniformly Accelerated Spherical Mirrors

TL;DR

This paper investigates quantum radiation emitted by small spherical mirrors undergoing uniform acceleration, using Euclidean methods and Green's functions to analyze vacuum fluctuations and energy flux.

Contribution

It introduces a novel approach to compute quantum radiation from accelerated spherical mirrors via Wick rotation and separation of variables in Euclidean space.

Findings

Derived the Hadamard function in the wave-zone regime.

Calculated vacuum fluctuations and energy density flux.

Provided a new method for analyzing quantum radiation from accelerated objects.

Abstract

We study quantum radiation generated by a uniformly accelerated motion of small spherical mirrors. To obtain Green's function for a scalar massless field we use Wick's rotation. In the Euclidean domain the problem is reduced to finding an electric potential in 4D flat space in the presence of a metallic toroidal boundary. The latter problem is solved by a separation of variables. After performing an inverse Wick's rotation we obtain the Hadamard function in the wave-zone regime and use it to calculate the vacuum fluctuations and the vacuum expectation for the energy density flux in the wave zone.