General relativistic stars: Polytropic equations of state

In this paper, the gravitational field equations for static spherically sym metric perfect fluid models with a polytropic equation of state, p = kp(1+1 n), are recast into two complementary 3-dimensional regular systems of ordi nary differential equations on compact state spaces. The systems are analyz ed numerically and qualitatively, using the theory of dynamical systems. Ce rtain key solutions are shown to form building blocks which, to a large ext ent determine the remaining solution structure. In one formulation. there e xists a monotone function that forces the general relativistic solutions to wards a part of the boundary of the state space that corresponds to the low pressure limit. The solutions on this boundary describe Newtonian models a nd thus the relationship to the Newtonian solution space is clearly display ed. It is numerically demonstrated that general relativistic models have fi nite radii when the polytropic index n satisfies 0 less than or equal to n less than or similar to 3.339 and infinite radii when n greater than or equ al to 5. When 3.339 less than or similar to n < 5, there exists a 1-paramet er set of models with finite radii and a finite number. depending on n. wit h infinite radii. 2000 Academic Press.