Conserved Quantities in Lemaitre-Tolman-Bondi Cosmology
  We study linear perturbations to a Lema{\^\i}tre-Tolman-Bondi (LTB)
background spacetime. Studying the transformation behaviour of the
perturbations under gauge transformations, we construct gauge invariant
quantities. We show, using the perturbed energy conservation equation, that
there are conserved quantities in LTB, in particular a spatial metric trace
perturbation, \zeta_{SMTP}, which is conserved on all scales. We then briefly
extend our discussion to the Lema{\^\i}tre spacetime, and construct
gauge-invariant perturbations in this extension of LTB spacetime.
