Orbits of light rays in scale-dependent gravity: Exact analytical solutions to the null geodesic equations
Grigoris Panotopoulos, Ángel Rincón, Ilídio Lopes
Abstract
We study photon orbits in the background of ($1+3$)-dimensional static, spherically symmetric geometries. In particular, we have obtained exact analytical solutions to the null geodesic equations for light rays in terms of the Weierstra\ss{} function for space-times arising in the context of scale-dependent gravity. The trajectories in the ($x\ensuremath{-}y$) plane are shown graphically, and we make a comparison with similar geometries arising in different contexts. The light deflection angle is computed as a function of the running parameter $\ensuremath{\xi}$, and an upper bound for the latter is obtained.
Topics & Concepts
GeodesicGeodesics in general relativityNull (SQL)PhysicsSolving the geodesic equationsScale (ratio)Mathematical analysisClassical mechanicsMathematicsComputer scienceQuantum mechanicsDatabaseCosmology and Gravitation TheoriesBlack Holes and Theoretical PhysicsAdvanced Differential Geometry Research