Charged Polytropic Fluid Spheres with a Cosmological Constant

Trapping of geodesics inside compact objects is a purely relativistic phenomenon that is of interest in astrophysics. In this paper, we study this phenomenon within charged polytropic configurations with a cosmological constant. We consider a static fluid sphere with a polytropic equation of state, $p \propto \rho^\Gamma$, and a charge distribution, $q(r)\propto r^n$. By analysing the physical properties of the fluid, we restrict ourselves to the configurations that are physically acceptable. Within these, we then explore the $n$-$\Gamma$ parameter space and find the trapping regions. Going beyond the traditionally studied case of null geodesics, we also study trapping of charged and/or massive particles. We show that for neutral null particles (and only for them), the trapping depends purely on the metric functions. In all the other cases, the particle properties such as their charge and/or energy also affect the trapping. We present all these cases and find that trapping of all types of particles is allowed for a broad range of values of $\Gamma$ and $n$.