Pressureless static solutions in a Newton-Yukawa gravity model

Non-minimally coupled curvature-matter gravity models are an interesting alternative to the Theory of General Relativity and address dark energy matter cosmological problems. These have complex field equations that prevent a full analytical study. Nonetheless, in particular limit, behavior distribution can, these models, be described by Schr\"odinger-Newton system. In nonlinear optics, system can used tackle wide variety relevant situations several numerical tools been developed for this purpose. Interestingly, methods adapted study problems as well its extensions. work, we report use non-minimal coupling model introduces two new potentials, attractive Yukawa potential repulsive proportional density. Using imaginary-time propagation method shown stationary solutions arise even at low density regimes.