ASYMPTOTICAL ANALYSIS OF THE EQUATIONS FOR THE SPINOR PARTICLE IN THE SCHWARZSCHILD FIELD
Abstract
For massless Dirac particles, the general mathematical study of the tunneling proccess of a particle through the effective potential barrier generated by the Schwarzschild black hole is made. Results are significantly different for two situations: first when a particle falls on the barrier from within and second when a particle falls on the barrier from the outside. The study is based on the use of 8 Frobenius solutions of the related second-order differential equations with the second-rank non- regular singularities. The mathematical structure of the derived asymptotic relations is exact, however the analytical expressions for the involved convergent powers series are not known. So, a further study should be based on the numerical summation of the series.
About the Authors
Y. А. RUSAK
Brest State University named after A. S. Pushkin
Belarus
Belarus
О. V. VEKO
Gymnasium, Kalinkovichi
Belarus
Belarus
Е. М. OVSIYUK
Mozyr State Pedagogical University named after I. P. Shamyakin
Belarus
Belarus
References
1. Regge, T. Stability of a Schwarzschild Singularity / T. Regge, J. A. Wheeler // Phys. Rev. – 1957. – Vol. 108, no. 4. – P. 1063–1069.
2. Chandrasekhar, S. The Mathematical Theory of Black Holes / S. Chandrasekhar. – Oxford: Oxford University Press, 1983.
3. Slavyanov, S. Yu. Special functions. A unified theory based on singularities / S. Yu. Slavyanov, W. Lay. – New York: Oxford University Press, 2000.
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