Motion of Particles and Gravitational Lensing Around (2+1)-dimensional BTZ black holes in Gauss-Bonnet Gravity

We study motion of test particles and photons in the vicinity of (2+1) dimensional Gauss-Bonnet (GB) BTZ black hole. We find that the presence of the coupling constant serves as an attractive gravitational charge, shifting the innermost stable circular orbits outward with respect to the one for this theory in 4 dimensions. Further we consider the gravitational lensing, to test the GB gravity in (2+1) dimensions and show that the presence of GB parameter causes the bending angle to grow up first with the increase of the inverse of closest approach distance, $u_0$, then have its maximum value for specific $u_0^*$, and then reduce until zero. We also show that increase in the value of the GB parameter makes the bending angle smaller and the increase in the absolute value of the negative cosmological constant produces opposite effect on this angle.

Quasi Periodic Oscillations of Test Particles and Red-Blue Shifts of the Photons Emitted By the Charged Test Particles Orbiting the Charged Black Hole in the Presence of Quintessence and Clouds of Strings

Here we examine the circular motion of test particles and photons in the spacetime geometry of charged black hole surrounded by quintessence and clouds of strings for the equation of state parameter $omega_q=-2/3$. We observe that there exist stable circular orbits in this geometry for very small values of the quintessence and string cloud parameters, i.e., $0<gamma<<1$ and $0<alpha<<1$. We observe that if the values of $gamma$ and $alpha$ increase, 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 $gamma$ and $alpha$. Further, we investigate the quasi-periodic oscillations of test particles near the stable circular orbits. With the increasing values of $Q$, the stable circular orbits get away from the central object; therefore, one can observe lower epicyclic frequencies away from the central gravitating source with the increase in the values of $Q$. The redshift parameter $z$ of the photons emitted by the charged test particles moving in the stable circular orbits around the central source increases with an increase in the parameter $alpha$ and decreases with an increase in the values of the charge $Q$. In the Banados-Silk-West (BSW) process study, we note that the centre of mass-energy at the horizon of this Riessner-Nordstrom black hole with quintessence and string clouds increases indefinitely if the charge of one of the colliding particles attains its critical value. 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 $alpha$, $gamma$ and $Q$ graphically.