General relativistic polytropes with a repulsive cosmological constant

Understand

Spherically symmetric equilibrium configurations of perfect fluid obeying a polytropic equation of state are studied in spacetimes with a repulsive cosmological constant.

• The configurations are specified in terms of three parameters---the polytropic index $n$, the ratio of central pressure and central energy density of matter $\sigma$, and the ratio of energy density of vacuum and central density of matter $\lambda$.
• The static equilibrium configurations are determined by two coupled first-order nonlinear differential equations that are solved by numerical methods with the exception of polytropes with $n=0$ corresponding to the configurations with a uniform distribution of energy density, when the solution is given in terms of elementary functions.
• The geometry of the polytropes is conveniently represented by embedding diagrams of both the ordinary space geometry and the optical reference geometry reflecting some dynamical properties of the geodesic motion.