Weak-field analytical solutions for f(R,L_matt) gravity in a static and spherically symmetric space-time for perfect fluids
We study the weak-field regime of $f(R,\lmatt)$ gravity for a static and spherically symmetric configuration described by a perfect fluid, whose energy density is perturbed about a constant reference value. By means of a weak-field limit expansion about a Minkowski geometric background and under a quasi-Newtonian approximation, we derive and analytically solve the coupled system that governs the gravitational perturbations and the matter variables. The solution contains the long-range Newtonian contribution and Yukawa-type corrections in the temporal and radial components of the metric. In the matter sector, the energy density, the internal energy, and the pressure acquire radial contributions, with a non-zero constant background rest-mass energy density and vanishing background internal energy and pressure. The results show how the non-minimal coupling between curvature and matter jointly modifies the geometry and the fluid in the considered regime.