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Register a new userOrbits of light rays in scale-dependent gravity: Exact analytical solutions to the null geodesic equations
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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 $(x-y)$ 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.
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This paper describes the Fortran 77 code SIMU, version 1.1, designed for numerical simulations of observational relations along the past null geodesic in the Lemaitre-Tolman-Bondi (LTB) spacetime. SIMU aims at finding scale invariant solutions of the average density, but due to its full modularity it can be easily adapted to any application which requires LTBs null geodesic solutions. In version 1.1 the numerical output can be read by the GNUPLOT plotting package to produce a fully graphical output, although other plotting routines can be easily adapted. Details of the codes subroutines are discussed, and an example of its output is shown.
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This note describes the behavior of null-geodesics near nondegenerate Killing horizons in language amenable to the application of a general framework, due to Vasy and Hintz, for the analysis of both linear and nonlinear wave equations. Throughout, the viewpoint of Melroses b-geometry on a suitable compactification of spacetime at future infinity is adopted.
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