Quantum radiation of uniformly accelerated spherical mirrors

We study quantum radiation generated by uniformly accelerated motion of small spherical mirrors. To obtain the Green 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 four-dimensional 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 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.