Gauge-invariant perturbations on most general spherically symmetric space-times

The Einstein field equations and the conservation equations linearized around a most general (astrophysically relevant) spherically symmetric space-time are reduced to a set of equations for gauge-invariant geometrical objects defined on the two-dimensional timelike submanifold spanned by the radial and time coordinates. Odd-parity metric and matter perturbations are each expressed in terms of a vector field, matter perturbations in terms of an additional scalar field on this submanifold. Even-parity perturbations are expressed in terms of a symmetric tensor field and a scalar field for the metric and in terms of two scalars, a vector, and a symmetric tensor field for matter. The odd-parity vectorial perturbations are derivable from a single master scalar equation, and their junction conditions across the surface of a collapsing star are given.