Massless Dirac particles in the vacuum C-metric

TL;DR

This paper investigates the behavior of massless Dirac particles in the vacuum C-metric spacetime, providing exact and perturbative solutions, and exploring the coupling between particle spin and spacetime acceleration.

Contribution

It offers the first exact solutions of the Dirac equation in the C-metric and establishes a connection with Kerr spacetime harmonics, highlighting spin-acceleration coupling effects.

Findings

Exact solutions in terms of Heun functions for Dirac particles

Acceleration-induced corrections to scattering cross sections

Mapping between acceleration harmonics and Kerr spheroidal harmonics

Abstract

We study the behavior of massless Dirac particles in the vacuum C-metric spacetime, representing the nonlinear superposition of the Schwarzschild black hole solution and the Rindler flat spacetime associated with uniformly accelerated observers. Under certain conditions, the C-metric can be considered as a unique laboratory to test the coupling between intrinsic properties of particles and fields with the background acceleration in the full (exact) strong-field regime. The Dirac equation is separable by using, e.g., a spherical-like coordinate system, reducing the problem to one-dimensional radial and angular parts. Both radial and angular equations can be solved exactly in terms of general Heun functions. We also provide perturbative solutions to first-order in a suitably defined acceleration parameter, and compute the acceleration-induced corrections to the particle absorption rate as well as to the angle-averaged cross section of the associated scattering problem in the low-frequency limit. Furthermore, we show that the angular eigenvalue problem can be put in one-to-one correspondence with the analogous problem for a Kerr spacetime, by identifying a map between these "acceleration" harmonics and Kerr spheroidal harmonics. Finally, in this respect we discuss the nature of the coupling between intrinsic spin and spacetime acceleration in comparison with the well known Kerr spin-rotation coupling.