Gravitational deflection of massive particles in Schwarzschild-de Sitter spacetime
Guansheng He, Xia Zhou, Zhong-Wen Feng, Xueling Mu, Hui Wang, Weijun Li, Chaohong Pan, Wenbin Lin
Abstract
Abstract 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 $$v_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>v</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> 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 $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> are dropped. The observable correctional effects due to the deviation of $$v_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>v</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> from light speed on the $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> -induced contributions to the deflection angle of light are also analyzed.