Gravitational deflection of massive particles in Schwarzschild-de Sitter spacetime

In this paper, the gravitational deflection of a relativistic massive neutral particle in the Schwarzschild-de Sitter spacetime is studied via the Rindler–Ishak method in the weak-field limit. When the initial velocity $$v_0$$ of the particle tends to the speed of light, the result is consistent with that obtained in the previous work for the light-bending case. Our result is reduced to the Schwarzschild deflection angle of massive particles up to the second order, if the contributions from the cosmological constant $$\varLambda $$ are dropped. The observable correctional effects due to the deviation of $$v_0$$ from light speed on the $$\varLambda $$ -induced contributions to the deflection angle of light are also analyzed.