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 non-rotating C-metric which encompass 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 equation for eigenfunctions and eigenvalues are explicitly solved.

References in corpus (7)

• Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions
• Interpreting the C-metric
• A new form of the C-metric
• The 192 Solutions of the Heun Equation
• On asymptotically flat solutions of Einstein's equations periodic in time II. Spacetimes with scalar-field sources
• A spectral method for half-integer spin fields based on spin-weighted spherical harmonics
• The Newtonian limit of spacetimes for accelerated particles and black holes

Cited by in corpus (11)

• Accelerating black holes: quasinormal modes and late-time tails
• Can test fields destroy the event horizon in the Kerr-Taub-NUT spacetime?
• Dynamical behavior of the $C$-metric: charged scalar fields, quasinormal modes and superradiance
• Quasinormal modes and stability of boosted Reissner-Nordström AdS black holes
• Light bending in a two black hole metric
• Hidden conformal symmetry for the accelerating Kerr black holes
• Separability of test fields equations on the C-metric background II. Rotating case and the Meissner effect
• On the nature of cosmic strings in black hole spacetimes
• Charged massless scalar fields in a charged $C$-metric black hole: Exact solutions, Hawking radiation, and scattering of scalar waves
• C-metric in a (nut)shell
• Cosmic strings in axisymmetric black hole spacetimes; the C--metric "engines"