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;