Static Charged Polytropic Spheres with a Cosmological Constant: Physical Acceptability and Trapped Orbits

We consider static charged fluid spheres with a cosmological constant. We assume a polytropic equation of state, $p \propto \rho^\Gamma$, and a power law charge distribution, $q\propto r^n$. Using this, we convert the generalised Tolman-Oppenheimer-Volkoff equation into a differential equation for the mass profile. By solving this equation numerically, we analyse both physical and geometric properties of charged polytropic fluid spheres for different values of $n$ and $\Gamma$. By imposing subluminal sound speeds and energy conditions, we restrict ourselves to configurations that are physically acceptable. Then, within these physical models, we study internal trapping of circular geodesics and find the trapping regions in the $n$-$\Gamma$ parameter space. Going beyond the traditionally studied case of null geodesics, we consider orbits of charged and/or massive particles as well. We show that for neutral null particles (and only for them), the possibility of internal trapping is determined purely through geometry. In the other three cases, properties such as the particle's own charge and/or energy also play a role. In general, we find that trapping of all types of particles is allowed for a broad range of $n$ and $\Gamma$.