Radial pulsations and dynamical stability of spherically symmetric perfect fluid configurations in spacetimes with a nonzero cosmological constant

The equation governing small radial oscillations and the related Sturm-Liouville eigenvalue equation for eigenmodes of the oscillations are determined for spherically symmetric configurations of perfect fluid in spacetimes with a nonzero cosmological constant. The Sturm-Liouville equation is then applied in the cases of spherically symmetric configurations with uniform distribution of energy density and polytropic spheres. It is shown that a repulsive cosmological constant rises the critical adiabatic index and decreases the critical radius under which the dynamical instability occurs.