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

TL;DR

This paper investigates how Gauss-Bonnet gravity influences particle motion and gravitational lensing around (2+1)-dimensional BTZ black holes, revealing effects of the GB parameter on orbits and light bending.

Contribution

It provides the first analysis of particle trajectories and lensing in (2+1)D Gauss-Bonnet BTZ black holes, highlighting the role of the GB coupling constant.

Findings

GB parameter acts as an attractive gravitational charge.

Innermost stable circular orbits shift outward with GB coupling.

Bending angle varies non-monotonically with closest approach distance.

Abstract

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.