Evolution of linear perturbations in spherically symmetric dust
  spacetimes
  We present results from a numerical code implementing a new method to solve
the master equations describing the evolution of linear perturbations in a
spherically symmetric but inhomogeneous background. This method can be used to
simulate several configurations of physical interest, such as relativistic
corrections to structure formation, the lensing of gravitational waves and the
evolution of perturbations in a cosmological void model. This paper focuses on
the latter problem, i.e. structure formation in a Hubble scale void in the
linear regime. This is considerably more complicated than linear perturbations
of a homogeneous and isotropic background because the inhomogeneous background
leads to coupling between density perturbations and rotational modes of the
spacetime geometry, as well as gravitational waves. Previous analyses of this
problem ignored this coupling in the hope that the approximation does not
affect the overall dynamics of structure formation in such models. We show that
for a giga-parsec void, the evolution of the density contrast is well
approximated by the previously studied decoupled evolution only for very
large-scale modes. However, the evolution of the gravitational potentials
within the void is inaccurate at more than the $10\%$ level, and is even worse
on small scales.
