A new approach for doing theoretical and numeric work with
  Lemaitre-Tolman-Bondi dust models
  We introduce quasi-local integral scalar variables for the study of
spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models. Besides
providing a covariant, and theoretically appealing, interpretation for the
parameters of these models, these variables allow us to study their dynamics
(in their full generality) by means of fluid flow evolution equations that can
be handled with simple numerical techniques and has a significant potential for
astrophysical and cosmological applications. These evolution equations can also
be understood in the framework of a gauge invariant and covariant formalism of
spherical non-linear perturbations on a FLRW background. The covariant time
splitting associated with the new variables leads, in a natural way, to
rephrase the known analytic solutions within an initial value framework in
which covariant scalars are given by simple scaling laws. By using this
re-parametrization of the analytic solutions, we re-examine and provide an
alternative outlook to various theoretical issues already treated in the
literature: regularity conditions, an Omega parameter, as well as the fitting
of a given LTB model to radial profiles of density or velocity at different
cosmic times. Other theoretical issues and numeric applications will be
examined in separate articles.
