Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1999-07-29
Class.Quant.Grav. 16 (1999) 3165-3181
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
RevTex, 11 Latex pages and 12 Figures ; Classical and Quantum Gravity (in Press) (1999)
Scientific paper
10.1088/0264-9381/16/10/309
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 the present paper, we solve the radial equations in a Schwarzschild geometry semi-analytically using Wentzel-Kramers-Brillouin approximation (in short WKB) method. Among other things, we present analytical expression of the instantaneous reflection and transmission coefficients and the radial wave functions of the Dirac particles. Complete physical parameter space was divided into two parts depending 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 equations by a Quantum Mechanical approach, in which the potential is approximated by a series of steps and found that these two solutions agree. We compare solutions of different initial parameters and show how the properties of the scattered wave depend on these parameters.
Chakrabarti Sandip K.
Mukhopadhyay Banibrata
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