Orbits of light rays in scale-dependent gravity: Exact analytical solutions to the null geodesic equations

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 Weierstraß function for space-times arising in the context of scale-dependent gravity. The trajectories in the $(x-y)$ 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 $\xi$, and an upper bound for the latter is obtained.

arXiv comment10 pages, 8 figures, accepted in PRD

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