Tolman VII Solution with Cosmological Constant and Charge

The Tolman VII space-time is one of the few physically acceptable space-times in general relativity and has been a basis for several neutron star models. We consider charged perfect fluid spheres with a cosmological constant and present a generalized Tolman VII solution. The solution exhibits a spherical spatial geometry for realistic values of cosmological constant and charge. We also find an analytical expression for the equation of state of the fluid. Performing numerical fitting, we find a polytropic equation of state equivalent to the one found analytically. Analyzing sound speed and energy conditions, we investigate the physical acceptability of the solution.