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 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.
Highlights
This conventional opinion had been believed for a long time until Rindler and Ishak [20] drew an opposite conclusion in 2007
We have extended the Rindler–Ishak approach to investigate the gravitational deflection of a relativistic massive particle in Schwarzschild-de Sitter geometry in the weak-field limit
On the basis of this approach, it is found that the cosmological constant appears in the orbital equation of a massive particle and contributes to its deflection angle
Summary
This conventional opinion had been believed for a long time until Rindler and Ishak [20] drew an opposite conclusion in 2007 They applied the invariant formula of cosine to achieve the Λ-induced contribution to the weak-field bending of light in the Schwarzschild-de Sitter (SdS) spacetime. There is no doubt that the presence of the Λ-induced effect on the orbital perihelion advance, verified by all these works, provides us an excellent basis for considering the gravitational lensing of massive particles due to Λ in turn. We adopt the Rindler–Ishak approach to calculate the gravitational deflection of a relativistic massive neutral particle up to the second post-Minkowskian (2PM) order in the SdS spacetime.
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