On the influence of the cosmological constant on trajectories of light and associated measurements in Schwarzschild de Sitter space

Abstract

In this paper we review and build on the common methods used to analyze null geodesics in Schwarzschild de Sitter space. We present a general technique which allows finding measurable intersection angles of null trajectories analytically, and as one of its applications we establish a general relativistic aberration relationship. The tools presented are used to analyze some standard setups of gravitational deflection of light and gain a clear understanding of the role that the cosmological constant, $\Lambda$, plays in gravitational lensing phenomena. Through reviewing some recent papers on the topic with the present results in mind, we attempt to explain the major sources of disagreement in the ongoing debate on the subject, which started with Rindler and Ishak's original paper, regarding the influence of $\Lambda$ on lensing phenomena. To avoid ambiguities and room for misunderstanding we present clear definitions of the quantities used in the present analysis as well as in other papers we discuss.

42 pages 18 figures revtex 4-1 twocolumn

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