  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.
