Solution of Dirac equation in Reissner-Nordstrom de Sitter space

The radial parts of the Dirac equation between the outer black hole horizon and the cosmological horizon are solved in Reissner-Nordstrom de Sitter (RNdS) space numerically. An accurate approximation, the polynomial approximation, is used to approximate the modified tortoise coordinate (r) over cap (*), which leads to the inverse function r = r ((r) over cap (*)) and the potential V((r) over cap (*)). The potential V((r) over cap (*)) is replaced by a collection of step functions in sequence. Then the solution of the wave equation as well as the reflection and transmission coefficients is computed by a quantum mechanical method.