The talk focuses on the study of linear perturbations to a Lemaitre-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 which is conserved on all scales, for barotropic fluids. We then briefly
extend our discussion to the Lemaitre spacetime, and construct
gauge-invariant perturbations in this extension of LTB spacetime. Some further questions surrounding LTB will be briefly discussed.