Pseudo-supersymmetric approach to the Dirac operator in the Schwarzschild spacetime

Abstract

We have discussed the Dirac equation in the Schwarzschild spacetime via pseudo-supersymmetric quantum mechanics and obtained the partner Hamiltonain of the initial Hamiltonian operator. We have shown that partner metric tensors of the corresponding Hamiltonians can be obtained through the intertwining relations of pseudo-supersymmetric approaches. Moreover, approximate solutions of the radial part are obtained within N = 2 supersymmetry and radial potential graphs are given, then, quasinormal modes are discussed in the limit of r → ±∞.