Publication date: Aug 2006
Abstract:
We determine the influence of a nonzero cosmological constant on
dynamical stability of spherically symmetric perfect fluid
configurations. The equations governing small radial oscillations and
the related Sturm-Liouville eigenvalue equation for eigenmodes of the
oscillations are generalised for the case of nonzero cosmological
constant. The Sturm-Liouville equation is then applied in the case of
polytropic equation of state. Based on this approach, the dependence of
the critical value of adiabatic index on relativistic parameter (defined
as ratio of central pressure to central energy density) is established
for values of polytropic index 3/2 and 3 and for both repulsive and
attractive cosmological constant using numerical computations. It is
shown that a repulsive cosmological constant rises the critical
adiabatic index and decreases the critical radius under which the
dynamical instability occurs.
Authors:
Hledík, S.; Stuchlík, Z.;