Motion of particles and gravitational lensing around the (2+1)-dimensional BTZ black hole in Gauss–Bonnet gravity

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, $$u_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>u</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> , reaching a peak value for a specific $$u_0^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>u</mml:mi><mml:mn>0</mml:mn><mml:mo>∗</mml:mo></mml:msubsup></mml:math> , 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.

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