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Circular orbit of a particle and weak gravitational lensing

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arxiv 2006.13047 v1 pith:7FX3XVAQ submitted 2020-06-21 gr-qc

Circular orbit of a particle and weak gravitational lensing

classification gr-qc
keywords blackcircularorbitdeflectionholeanglegravitationalgravity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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The purpose of this paper is twofold. First, we introduce a geometric approach to study the circular orbit of a particle in static and spherically symmetric spacetime based on Jacobi metric. Second, we apply the circular orbit to study the weak gravitational deflection of null and time-like particles based on Gauss-Bonnet theorem. By this way, we obtain an expression of deflection angle and extend the study of deflection angle to asymptotically non-flat black hole spacetimes. Some black holes as lens are considered such as a static and spherically symmetric black hole in the conformal Weyl gravity and a Schwarzschild-like black hole in bumblebee gravity. Our results are consistent with the previous literature. In particular, we find that the connection between Gaussian curvature and the radius of a circular orbit greatly simplifies the calculation.

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Cited by 3 Pith papers

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