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

Abstract

The generalized Schrödinger-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.

arXiv comment5 pages, 4 figures

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• Cassini and extra force constraints to nonminimally coupled gravity with screening mechanism
• Pressureless stationary solutions in a Newton-Yukawa gravity model
• Theories of gravity with nonminimal matter-curvature coupling and the de Sitter swampland conjectures
• Black Hole Solutions in Non-Minimally Coupled Weyl Connection Gravity
• Weak Field Limit of the Nonminimally Coupled Weyl Connection Gravity
• Testing the Dark Universe through the Layzer-Irvine Equation