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The equation of motion of a massless Dirac particle in the  C -metric leads to the general Heun equation (GHE) for the radial and the polar variables. The GHE, under certain parametric conditions, is cast in terms of a new set of  su (1, 1) generators involving differential operators of  degrees  ±1/2 and 0. Additional  Heun polynomials  are obtained using this new algebraic structure and are used to construct some exact solutions for the radial and the polar parts of the Dirac equation.

Heun Polynomials and Exact Solutions for the Massless Dirac Particle in the C -Metric