Massless fermions on static general prolate metrics and their Heun solutions

Employing a pseudo-orthonormal coordinate-free approach we write down the Dirac equation in spacetimes with static generally prolate metrics. As examples, we consider the electrically charged C-metric, the vacuum C-metric, the Reissner-Nordstrom and Schwarszchild spacetimes and the BBMB black hole and show that the solutions to the Dirac equations for particles these spacetimes can be derived in terms of Heun's general functions and their confluent and double confluent forms.