Abstract
In this paper, we present an approximate analytic solution to the Dirac equation in the Schwarzschild geometry to investigate the Zitterbewegung (ZB) effect. The analytical expression for the current density, which is induced by the motion of a wave packet of electrons, is obtained. In addition, the intensity of dipole radiation near the black hole is calculated. The proposed approach is based on the Schrödinger representation, thereby allowing to consider the ZB effect in the case of a curved space. The considered example demonstrates a possibility for applying this approach to astrophysical applications, in particular to problems of the electron radiation in the vicinity of real black holes.
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