Gravitational lensing effect in the Universe with a Finsler background

Abstract

The gravitational deflection of light is a common effect for the massive objects in galactic astronomy. Recently, several universal models with Finsler background were introduced to solve the abnormal phenomena. In this manuscript, we consider the deflection of gravitational lens in a general Finsler space. Firstly, with the assistance of the Landsberg angle, we introduce four definitions of the deflection angle, which are not equal mutually in general case. Secondly, we introduce an important concept called asymptotically symmetric Minkowskian flat (ASMF) manifold, on which we define the global normal deflection angle (GNDA) as well as the global tangent deflection angle (GTDA). Lastly, we present an integral expression of the GNDA on an ASMF manifold. This result suggests to us that the non-Riemannian Finsler quantities may contain the information of dark matter.