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The generalized Schr\"odinger-Newton system of equations with both local andnonlocal nonlinearities is widely used to describe light propagating innonlinear media under the paraxial approximation. However, its use is notlimited to optical systems and can be found to describe a plethora of differentphysical phenomena, for example, dark matter or alternative theories forgravity. Thus, the numerical solvers developed for studying light propagatingunder this model can be adapted to address these other phenomena. Indeed, inthis work we report the development of a solver for the HiLight simulationsplatform based on GPGPU supercomputing and the required adaptations for thissolver to be used to test the impact of new extensions of the Theory of GeneralRelativity in the dynamics of the systems, in particular those based ontheories with non-minimal coupling between curvature and matter. This approachin the study of these new models offers a quick way to validate them sincetheir analytical analysis is difficult. The simulation module, its performance,and some preliminary tests are presented in this paper.

Using numerical methods from nonlocal optics to simulate the dynamics of N-body systems in alternative theories of gravity