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.

Jeans instability in non-minimal matter-curvature coupling gravity

“…These results are the basis for numerical solvers from nonlocal optics to simulate the dynamics of N-body systems in the non-minimal matter-curvature coupling model of Refs. [24,25], as they allow the study of weak field implications from modified gravity in the context of gravitational collapse. Furthermore we note that issues concerning stellar stability from modified Lane-Emden equation were addressed for the case of f(R) theories in Refs.…”

“…Hence, we can henceforth neglect it. We should note that if we aimed at studying the weak field implications of the non-minimal coupling effects, we would find that these are measurable and lead to important signatures, such as a stronger gravitational pull [23], and shock waves in gravitational collapse [24,25]. Therefore, we can recast the first equality of Eq.…”

“…In fact, we can study unstable (Re(ω) = 0 ∧ Im(ω) > 0), neutrally stable (Re(ω) = 0 ∧ Im(ω) = 0) and Landau damped solutions (|Im(ω)/Re(ω)| O(1)) from the dispersion relation, Eq. (25). In this work, we are interested in the unstable modes.…”

“…In the weak field regime, this model yields a correction to the Newtonian potential [23], and presents shock waves in the gravitational collapse [24,25]. It has been recently applied to the generalisation of the Boltzmann equation for such scenario and its main implications were analysed in Ref.…”

Pressureless stationary solutions in a Newton-Yukawa gravity model

“…The non-minimal coupling gives rise to very convoluted field equations that cannot, in general, be treated analytically and poses challenges to the existing numerical methods. However, as previously shown [3], under the right assumptions, the field equations for specific matter distributions can be transformed into a Schrödinger-Newton system of equations.…”