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We present results from a numerical code implementing a new method to solvethe master equations describing the evolution of linear perturbations in aspherically symmetric but inhomogeneous background. This method can be used tosimulate several configurations of physical interest, such as relativisticcorrections to structure formation, the lensing of gravitational waves and theevolution of perturbations in a cosmological void model. This paper focuses onthe latter problem, i.e. structure formation in a Hubble scale void in thelinear regime. This is considerably more complicated than linear perturbationsof a homogeneous and isotropic background because the inhomogeneous backgroundleads to coupling between density perturbations and rotational modes of thespacetime geometry, as well as gravitational waves. Previous analyses of thisproblem ignored this coupling in the hope that the approximation does notaffect the overall dynamics of structure formation in such models. We show thatfor a giga-parsec void, the evolution of the density contrast is wellapproximated by the previously studied decoupled evolution only for verylarge-scale modes. However, the evolution of the gravitational potentialswithin the void is inaccurate at more than the $10\%$ level, and is even worseon small scales.

Evolution of linear perturbations in spherically symmetric dust spacetimes