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The solution of Dirac equation in quasi-extreme Reissner-Nordström de Sitter space. (English) Zbl 1181.83127

Summary: The radial parts of Dirac equation between the outer black hole horizon and the cosmological horizon in quasi-extreme Reissner-Nordström de Sitter (RNdS) geometry is solved numerically. We use an accurate polynomial approximation to mimic the modified tortoise coordinate \(\hat r_*(r)\), for obtaining the inverse function \(r = r(\hat r_*)\) and \(V = V(\hat r_*)\). We then use a quantum mechanical method to solve the wave equation and give the reflection and transmission coefficients. We concentrate on two limiting cases. The first case is when the two horizons are close to each other, and the second case is when the horizons are far apart.

MSC:

83C57 Black holes
83C22 Einstein-Maxwell equations
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
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