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

TL;DR

This paper develops a GPU-accelerated numerical solver based on nonlocal optics methods to simulate N-body systems in alternative gravity theories, enabling rapid testing of complex models with difficult analytical solutions.

Contribution

It introduces a novel GPU-based solver for nonlocal optics equations adapted to simulate alternative gravity theories with non-minimal coupling.

Findings

Solver successfully implemented on GPGPU platform.

Preliminary tests demonstrate computational efficiency.

Framework adaptable to various extended gravity models.

Abstract

The generalized Schr\"odinger-Newton system of equations with both local and nonlocal nonlinearities is widely used to describe light propagating in nonlinear media under the paraxial approximation. However, its use is not limited to optical systems and can be found to describe a plethora of different physical phenomena, for example, dark matter or alternative theories for gravity. Thus, the numerical solvers developed for studying light propagating under this model can be adapted to address these other phenomena. Indeed, in this work we report the development of a solver for the HiLight simulations platform based on GPGPU supercomputing and the required adaptations for this solver to be used to test the impact of new extensions of the Theory of General Relativity in the dynamics of the systems, in particular those based on theories with non-minimal coupling between curvature and matter. This approach in the study of these new models offers a quick way to validate them since their analytical analysis is difficult. The simulation module, its performance, and some preliminary tests are presented in this paper.