Semi-analytical solution of Dirac equation in Schwarzschild geometry

Separation of the Dirac equation in the spacetime around a Kerr black hole into radial and angular coordinates was done by Chandrasekhar in 1976. In t he present paper, we solve the radial equations in a Schwarzschild geometry semi-analytically using the WKB approximation method. Among other things, we present an analytical expression of the instantaneous reflection and tra nsmission coefficients and the radial wave functions of the Dirac particles . The complete physical parameter space was divided into two parts dependin g on the height of the potential well and energy of the incoming waves. We show the general solution for these two regions. We also solve the equation s using a quantum mechanical approach in which the potential is approximate d by a series of steps and we have found that these two solutions agree. We compare solutions of different initial parameters and show how the propert ies of the scattered wave depend on these parameters.