Stabilizing Spherical Energy Shells with Angular Momentum in
  Gravitational Backgrounds
  Spherical energy shells in General Relativity tend to collapse due to
gravitational effects and/or due to tension effects. Shell stabilization may be
achieved by modifying the gravitational properties of the background spacetime.
Thus, gravastars consist of stiff matter shells with an interior deSitter space
and an exterior Schwarzshild spacetime whose attractive gravity balances the
interior repulsive gravity of the interior deSitter spacetime leading to a
stable stiff matter shell. Similar stabilization effects may be achieved by
considering rotating shells. Here we study the stability of slowly rotating
fluid shells. We show that the angular velocity of the shell has stabilizing
properties analogous to the repulsive deSitter gravity of the interior of a
gravastar. We thus use the Israel junction conditions and the fluid equation of
state of the rotating shell to construct the dynamical equations that determine
the evolution of the rotating shell radius. These dynamical equations depend on
the parameters of the background spacetime and on the angular velocity of the
shell. Assuming a rotating interior and a Schwarzschild exterior spacetime we
show that the angular velocity of the shell has interesting stabilizing
properties on the evolution of its radius R. Thus rotating matter (or vacuum)
shells can imitate black holes while avoiding the presence of a singularity and
without the presence of an interior deSitter space.
