Gravitational deflection of massive particles in Schwarzschild-de Sitter spacetime
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Regular Article - Theoretical Physics
Gravitational deflection of massive particles in Schwarzschild-de Sitter spacetime Guansheng He1,a , Xia Zhou2 , Zhongwen Feng2 , Xueling Mu3 , Hui Wang4,5 , Weijun Li1, Chaohong Pan1,b , Wenbin Lin1,4,c 1
School of Mathematics and Physics, University of South China, Hengyang 421001, China Physics and Space Science College, China West Normal University, Nanchong 637009, China 3 School of information science and Engineering, Chengdu University, Chengdu 610106, China 4 School of Physical Science and Technology, Southwest Jiaotong University, Chengdu 610031, China 5 Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Xinjiang 830011, China
2
Received: 26 June 2020 / Accepted: 18 August 2020 © The Author(s) 2020
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 v0 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 Λ are dropped. The observable correctional effects due to the deviation of v0 from light speed on the Λ-induced contributions to the deflection angle of light are also analyzed.
1 Introduction Since its original proposal by Einstein [1] for cosmological reasons in 1917, the cosmological constant Λ plays an important historical role in modern astronomy. Nowadays, much attention has been paid to it again with the consideration that the cosmological constant (or, more generally, dark energy) is regarded to be one of the main candidates responsible for the acceleration of the cosmic expansion (see, e.g., Refs. [2– 12], and references therein). Being a special gravitational source, Λ should exhibit its effect in all of the gravitational phenomenons such as the classical tests of general relativity. In 1983, Islam [13] placed constrains on the absolute value of Λ by calculating the advance of Mercury’s perihelion in the Kottler geometry [14] to get its upper limit. Meanwhile, the author gave a significant conclusion that the grava e-mail:
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itational deflection of light is independent on Λ, which was later approved by many groups (see, for instance, Refs. [15– 19], and references therein). 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. Dramatically, their conclusion that Λ does contribute to light bending has been recently confirmed by various auth
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