Abstract
The radial parts of the Dirac equation between the inner and the outer horizon in Schwarzschild–de Sitter geometry are solved. Two limiting cases are concerned. The first case is when the two horizons are far apart and the second case is when the horizons are close to each other. In each case, a ‘tangent’ approximation is used to replace the modified ‘tortoise’ coordinate r*, which leads to a simple analytically invertible relation between r* and the radius r. The potential V(r*) is replaced by a collection of step functions in sequence. Then the solutions of the wave equation as well as the reflection and transmission coefficients are computed by a quantum mechanical method.
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