Publication date: Dec 2004
Abstract:
Solutions of general relativistic field equations for static,
spherically symmetric, equilibrium perfect-fluid configurations obeying
the polytropic and adiabatic equation of state in the presence of a
repulsive cosmological constant are discussed. The influence of the
cosmological constant on the total mass of the configurations, their
radius and the profiles of energy density, rest energy density, pressure
and metric coefficients is studied and compared for the polytropic and
adiabatic case. The static equilibrium configurations are allowed for
σ<σ_{crit} (α<α_{crit}), where the
critical values σ_{crit} (α_{crit}) of the relativity
parameter σ (α) ≡ pcent/rhocent c^{2} of the
polytropes (adiabates) depend on the cosmological constant and the
polytropic index n of the equation of state and can be determined by a
numerical procedure. The numerical results show that for sufficiently
small values of the relativity parameter σ=α≪
σ_{crit}, the polytropic spheres are more compact than the
adiabatic ones. Increase of the cosmological constant causes increase of
both the radius and mass of the spheres and makes the profiles of the
metric coefficients flatter. For large values of the relativity
paramater, σ=α≲ σ_{crit}, the situation is more
complex and depends also on the value of the polytropic parameter n. The
mass of the adiabatic spheres can exceed the mass of the polytropes for
n≳ 2. In the case of n=3, the adiabatic spheres can even be more
compact than the polytropic ones. Generally, the role of the
cosmological constant is supressed with both σ=α and n
growing.
Authors:
Hledík, Stanislav; Stuchlík, Zdeněk; Mrázová, Kristina;