Classes of exact solutions for the massless Dirac particle in the $C$-metric

TL;DR

This paper finds exact polynomial solutions for the massless Dirac equation in the accelerating black hole spacetime, revealing algebraic structures that facilitate solving complex differential equations.

Contribution

It introduces classes of solutions to the Dirac equation in the C-metric using the algebraic properties of the general Heun equation, a novel approach in this context.

Findings

Derived (quasi-)polynomial solutions for the Dirac equation

Linked solutions to the general Heun equation

Exploited $su(1,1)$ algebraic structures for solution construction

Abstract

The massless Dirac particle in the $C$-metric, representing the exterior gravitational field of a uniformly accelerating black hole, is studied. Classes of (quasi-)polynomial solutions to the radial and the polar parts of the Dirac equation, each of which is equivalent to the general Heun equation~(GHE), are obtained exploiting the underlying $su(1,1)$ algebraic structures of the GHE.