The local - coordinate method is used to investigate the synchrotron radiation of ultrarelativistic particles moving in a magnetic field in curved space-time. General covariant formulas are obtained for the radiation spectrum in the classical and quantum cases. It is shown that the radiation intensity and the relative values of the quantum corrections increase when the particle moves close to the event horizons in the Schwartzschild metric. The limiting transition to conditions of geodesic synchrotron radiation is considered.
Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia
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