Intrinsic conformal symmetries in Szekeres models

Abstract

We show that Spatially Inhomogeneous (SI) and Irrotational dust models admit a six-dimensional algebra of Intrinsic Conformal Vector Fields (ICVFs) [Formula: see text] satisfying [Formula: see text], where [Formula: see text] is the associated metric of the two-dimensional distribution [Formula: see text] normal to the fluid velocity [Formula: see text] and the radial unit space-like vector field [Formula: see text]. The Intrinsic Conformal (IC) algebra is determined for each of the curvature value [Formula: see text] that characterizes the structure of the screen space [Formula: see text]. In addition the conformal flatness of the hypersurfaces [Formula: see text] indicates the existence of a ten-dimensional algebra of ICVFs of the three-dimensional metric [Formula: see text]. We illustrate this expectation and propose a method to derive them by giving explicitly the seven proper ICVFs of the Lemaître–Tolman–Bondi (LTB) model which represents the simplest subclass within the Szekeres family.