Abstract
We study the motion of test particles and photons in the vicinity of the (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 four dimensions. Further, we consider the gravitational lensing, to test the GB gravity in (2+1) dimensions and show that the presence of the GB parameter causes the bending angle to first increase with the increase in the inverse of the closest approach distance, u_0, reaching a peak value for a specific u_0^*, and then decreasing to zero. We also show that the increase in the value of the GB parameter decreases the bending angle, and the increase in the absolute value of the negative cosmological constant produces an opposite effect on this angle.
Highlights
Gravity theories can provide a useful tool to understand the nature of the gravitational interaction [4,5,6]
It is apparent from the figure that the increase in the GB parameter decreases the distance of closest approach slightly, while the increase in the absolute value of the cosmological constant shows the opposite effect
We have seen that the GB parameter has an opposite effect on the radii of stable circular orbits with respect to the cosmological constant
Summary
According to Lovelock’s theorem, in less than five dimensions the cosmological constant can only appear within general relativity [7]. Reference [12] is devoted to studying the classical spinning test particle motion around a non-rotating black hole in 4D EGB gravity. We plan to study the spacetime properties around the 3D Gauss–Bonnet BTZ black hole using the analysis of test particles and photon motion. We study the test particle motion around the 3D BTZ black hole in EGB theory in Sect. It is clearly seen that the integration constant m is a positive quantity, as takes negative values only Note that this AdS radius coincides with the one for the 3D BTZ black hole in Einstein gravity in the limit J → 0 [135]. We further consider positive values of α to explore the properties of the 3D BTZ black hole in GB gravity
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