Quasi-periodic oscillations of test particles and red–blue shifts of photons in the charged-Kiselev black hole with cloud of strings

Abstract

Here we examine the circular motion of test particles and photons in the spacetime geometry of the charged black hole surrounded by quintessence and clouds of strings for the equation of state parameter ω q = − 2 / 3 . We observe that there exist stable circular orbits in this geometry for very small values of the quintessence and the string cloud parameters, i.e., 0 < γ < < 1 and 0 < α < < 1 . We also observe that if the values of γ and α get increase, then the test particle can more easily escape the gravitational field of the black hole. While the effect of the charge Q of the black hole on the effective potential is just opposite to that of the parameters γ and α . Further we investigate the quasi-periodic oscillations of test particles near the stable circular orbits in the vicinity of the black hole considered here. With the increasing values of Q , the stable circular orbits move away from the central black hole, therefore, one can observe lower epicyclic frequencies away from the central gravitating source with the increase in the values of Q . The stable circular orbits get closer to the central object as the parameters γ and α increases. Thus, one can observe the epicyclic frequencies closer to the central object and would be higher as compared to the epicyclic frequencies observed in the case of pure Riessner-Nordstrom black hole, i.e., without quintessence and string clouds. The redshift parameter z , of the photons emitted by the charged test particles moving in the stable circular orbits around the charged quintessential black hole with clouds of strings, increases with an increase in the values of the parameter α and decreases with an increase in the values of the charge Q of the black hole. For different values of the parameter γ , it stays constant. In the study of the Banados-Silk-West (BSW) process, in the spacetime geometry of the charged-Kiselev black hole with string cloud, we notice that the centre-of-mass energy at the horizon of the black hole increases indefinitely if the charge of one of the colliding particles attains its critical value. We observe that the effective force on the test particles decreases as the values of the parameters γ and α go on increasing, and it increases with the increasing values of the charge Q of the black hole. For a better understanding of the study, we show the dependence of the radii of the circular orbits, energy and angular momentum of the particles, effective potential, effective force, quasi-periodic oscillations and red-blue shifts of photons of the test particles in the circular orbits on the parameters α , γ and Q graphically. • We have examined the circular motion of test particles and photons for the spacetime with a charged black hole surrounded by quintessence and clouds of strings. • We observe that if the values of γ and α increase, the test particle can more easily escape the gravitational field of the black hole. • With the increasing values of Q , the stable circular orbits move away from the central black hole. • The epicyclic frequencies closer to the central object would be higher than the epicyclic frequencies observed in the case of the pure Riessner-Nordstrom black hole. • The redshift parameter z of the photons emitted by the charged test particles moving in the stable circular orbits around the black hole.