Kerr black hole surrounded by a cloud of strings and its weak gravitational lensing in Rastall gravity

In this paper, an exact solution of the Kerr black hole surrounded by a cloud of strings in Rastall gravity is obtained by the Newman-Janis algorithm without complexification, and the influence of the string parameter a0 on black hole thermodynamics is studied. Furthermore, according to this black hole solution, we investigate the effect of a cloud of strings on the gravitational deflection of massive particles. For a receiver and a source at infinite distance from the lens object, we use an osculating Riemannian manifold method. While the distance is finite, we apply the generalized Jacobi metric method. For both of the two situations, the Jacobi-Maupertuis-Randers-Finsler metric and Gauss-Bonnet theorem are employed. It is found that the string parameter a0 has obvious modification on the gravitational deflection of massive particles. Our result is reduced to the deflection angle of light by the Kerr black hole surrounded by a cloud of strings in general relativity.