Publication date: Dec 2005
Equilibrium configurations that are solutions of spherically symmetric
hydrostatic equations of General Relativity for an ideal fluid obeying a
polytropic (or adiabatic) equation of state are given in the framework
of general relativity. The equilibrium configurations are given in
terms of the polytropic index n and the so called relativistic parameter
σ (for polytropes) or α (for adiabates).
First, simple models of polytropic and adiabatic spheres for
non-relativistic and ultra-relativistic case of the equation of state
are introduced. Then, the comparison of polytropic and adiabatic spheres
is given in some special characteristic cases and the influence of the
relativistic parameter on the structure of the spheres and the
gravitational and binding energy.
Mrázová, Kristina; Hledík, Stanislav; Stuchlík, Zdeněk;