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arXiv · 1611.09781

Intrinsic Conformal Symmetries in Szekeres models

Pantelis S. Apostolopoulos
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Abstract

We show that Spatially Inhomogeneous (SI) and Irrotational dust models admit a \emph{6-dimensional algebra } of \emph{Intrinsic Conformal Vector Fields} (ICVFs) $\mathbf{X}_{α}$ satisfying $p_{a}^{c}p_{b}^{d}\mathcal{L}_{\mathbf{X}_{α}}p_{cd}=2ϕ(\mathbf{X}_{α})p_{ab}$ 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\^ıtre-Tolman-Bondi (LTB) model which represents the simplest subclass within the Szekeres family.

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BibTeXRIS

Pantelis S. Apostolopoulos. 2017-05-22. Intrinsic Conformal Symmetries in Szekeres models. https://doi.org/10.1142/s0217732317500997

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