Intrinsic Conformal Symmetries in Szekeres models

We show that Spatially Inhomogeneous (SI) and Irrotational dust models admit a \emph{6-dimensional algebra } of \emph{Intrinsic Conformal Vector Fields} (ICVFs) ${\mathbf{X}}_{\alpha }$ satisfying $p_{a}^{c}p_{b}^{d}$\mathcal{L}${$\mathbf{X}${\alpha }}p_{cd}=2\phi ($\mathbf{X}${\alpha })p{ab}$where$p_{ab}$ is the associated metric of the 2d distribution $\mathcal{X}$ normal to the fluid velocity $u^a$ and the radial unit spacelike vector field $x^a$. The Intrinsic Conformal (IC) algebra is determined for each of the curvature value $ϵ$ that characterizes the structure of the screen space $\mathcal{X}$. In addition the conformal flatness of the hypersurfaces $\mathbf{u}=\mathbf{0}$ indicates the existence of a \emph{% 10-dimensional algebra} of ICVFs of the 3d metric $h_{ab}$. We illustrate this expectation and propose a method to derive them by giving explicitly the \emph{7 proper} ICVFs of the Lema^{\i}tre-Tolman-Bondi (LTB) model which represents the simplest subclass within the Szekeres family.