Relativistic equations for aspherical gravitational collapse

A totally gauge-invariant formulation of the linearized Einstein field equations for the most general matter-associated perturbations away from a spatially isotropic homogeneous space-time is given. We introduce metric, stress-energy, velocity, and scalar perturbation quantities that are invariant with respect to infinitesimal coordinate transformations on the background space-time. The linearized field equations as well as conservation equations are exhibited for the most general type of matter-associated perturbation; no gauge assumptions are made. In terms of the gauge-invariant perturbations these equations become very simple. This gauge-invariant formalism is then applied to a space-time permeated by a perfect fluid.