Separability of test fields equations on the C-metric background

Abstract

In the Kerr-Newman spacetime the Teukolsky master equation, governing the fundamental test fields, is of great importance. We derive an analogous master equation for the nonrotating C-metric which encompasses a massless Klein-Gordon field, neutrino field, Maxwell field, Rarita-Schwinger field and gravitational perturbations.

This equation is shown to be separable in terms of "accelerated spin-weighted spherical harmonics." It is shown that, contrary to ordinary spin-weighted spherical harmonics, the "accelerated" ones are different for different spins. In some cases, the equations for eigenfunctions and eigenvalues are explicitly solved.

Keywords

• uniformly accelerated particles
• rotating black hole
• general-relativity
• electromagnetic-fields
• formulation
• mass