Frequency Shift of Photons in Reissner-Nordström Black Hole Immersed in Perfect Fluid Dark Matter

Abstract

In this paper, we investigate the frequency shift of photons emitted by massive particles in stable circular orbits around a Reissner-Nordström black hole immersed in Perfect Fluid Dark Matter (PFDM). We use a relativistic formulism to derive an expression of the total red/blue shifts in terms of the Reissner-Nordström mass, electric charge and the PFDM parameter. We consider emitters in circular orbits around a charged black hole, which is the case for many stars revolving supermassive black holes at the center of galaxies. The obtained expression shed the light on the effect of the existence of PFDM on the stable circular orbits and frequency shifts.