Energy shift maps for direct photon emission by a particle orbiting a Schwarzschild black hole

Abstract

We examine the radiation emitted by a particle moving in a Schwarzschild spacetime. We treat the emitted radiation as photons that move along null geodesics. In this work, we calculate the energy shift of photons propagating from an emitting particle to a far away observer. This energy shift quantifies the photon's energy influenced by the spacetime curvature and the Doppler effects arising from the motion of the emitting particle. We find that if a distant observer is coplanar with the emitting particle, the energy shift of photons as observed by a distant observer takes its extremum values. We also find that the value of the energy shift approaches zero as the emitting particle approaches the photon sphere region.