Separability of test fields equations on the C-metric background II. Rotating case and the Meissner effect

TL;DR

This paper demonstrates the separability of the Teukolsky equation for arbitrary spin fields on a rotating C-metric background and confirms the Meissner effect in this context, showing magnetic field expulsion at extremal rotation.

Contribution

It extends the separability analysis of test fields to the rotating C-metric and confirms the Meissner effect for electromagnetic fields in this setting.

Findings

Teukolsky equation is separable on the rotating C-metric

Debye potential equations are separable and simplified

Magnetic fields are expelled at extremal rotation, confirming the Meissner effect

Abstract

We present the separation of the Teukolsky master equation for the test field of arbitrary spin on the background of the rotating C-metric. We also summarize and simplify some known results about Debye potentials of these fields on type D background. The equation for the Debye potential is also separated. Solving for the Debye potential of the electromagnetic field we show that on the extremely rotating C-metric no magnetic field can penetrate through the outer black hole horizon --- we thus recover the Meissner effect for the C-metric.