Quasi-local variables and inhomogeneous cosmological sources with   spherical symmetry
  We examine a large class of inhomogeneous spherically symmetric spacetimes that generalize the Lemaitre-Tolman-Bondi dust solutions to nonzero pressure ("LTB spacetimes"). Local covariant LTB objects can be expressed as perturbations of covariant quasi-local (QL) scalars that satisfy evolution equations of equivalent Friedman-Lemaitre-Robertson-Walker (FLRW) scalars. Thus, the dynamics of these spacetimes can be rigorously described as non-linear, gauge invariant and covariant perturbations on a formal FLRW background given by the QL scalars. Since LTB spacetimes are compatible with a wide variety of "equations of state" and theoretical assumptions, they provide an ideal framework for numerical models of cosmological sources under idealized but fully non-linear conditions. As an illustrative example, we briefly examine the formation of a black hole in an expanding Chaplygin gas universe. 
Roberto A. Sussman