The finitedistance gravitational deflection of massive particles in stationary spacetime: a Jacobi metric approach
Abstract
In this paper, we study the weak gravitational deflection of relativistic massive particles for a receiver and source at finite distance from the lens in stationary, axisymmetric and asymptotically flat spacetimes. For this purpose, we extend the generalized optical metric method to the generalized Jacobi metric method by using the JacobiMaupertuis RandersFinsler metric. More specifically, we apply the GaussBonnet theorem to the generalized Jacobi metric space and then obtain an expression for calculating the deflection angle, which is related to Gaussian curvature of generalized optical metric and geodesic curvature of particles orbit. In particular, the finitedistance correction to the deflection angle of signal with general velocity in the the Kerr black hole and Teo wormhole spacetimes are considered. Our results cover the previous work of the deflection angle of light, as well as the deflection angle of massive particles in the limit for the receiver and source at infinite distance from the lens object. In Kerr black hole spacetime, we compared the effects due to the black hole spin, the finitedistance of source or receiver, and the relativistic velocity in microlensings and lensing by galaxies. It is found in these cases, the effect of black hole spin is usually a few orders larger than that of the finitedistance and relativistic velocity, while the relative size of the latter two could vary according to the particle velocity, source or observer distance and other lensing parameters.
 Publication:

European Physical Journal C
 Pub Date:
 February 2020
 DOI:
 10.1140/epjc/s1005202076658
 arXiv:
 arXiv:1912.05194
 Bibcode:
 2020EPJC...80..157L
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 16 pages, 4 figures