Semi-analytical solution of Dirac equation in Schwarzschild geometry

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By this: publisher
In this Subject: Nuclear Physics
By this author: Mukhopadhyay B. ;&nbsp; Chakrabarti S.K.

Authors: Mukhopadhyay B.; Chakrabarti S.K.

Source: Classical and Quantum Gravity, Volume 16, Number 10, 1999 , pp. 3165-3181(17)

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Abstract:

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 the WKB approximation method. Among other things, we present an analytical expression of the instantaneous reflection and transmission coefficients and the radial wave functions of the Dirac particles. The 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 using a quantum mechanical approach in which the potential is approximated 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 properties of the scattered wave depend on these parameters.

Language: English

Document Type: Miscellaneous

Publication date: 1999-01-01