Modeling Polytropic Stars in General Relativity with a Cosmological Constant

Spherically symmetric compact objects are one of the most interesting solutions in General Relativity. In this project, we analyze solutions with a generalized polytropic equation of state and a cosmological constant. We derive a generalized Tolman-Oppenheimer-Volkoff equation, using which we convert the Einstein field equations into a differential equation for the mass profile of the star. This equation is highly nonlinear and it is impractical to solve it analytically. We find a few simple numerical solutions corresponding to particular values of polytropic index while analyzing the physical acceptability and the spacetime properties of solutions.