Intrinsic Conformal Symmetries in Szekeres models

Abstract

We show that Spatially Inhomogeneous (SI) and Irrotational dust models admit a \emph{6-dimensional algebra } of \emph{Intrinsic Conformal Vector Fields} (ICVFs) ${\mathbf{X}}_{\alpha }$ satisfying $p_a^c{p}_b^d{\mathcal{L}}_{{\mathbf{X}}_{\alpha }}{p}_{cd}=2\varphi ({\mathbf{X}}_{\alpha })p_{ab}$ 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 $\epsilon$ that characterizes the structure of the screen space $\mathcal{X}$. In addition the conformal flatness of the hypersurfaces $\mathbf{u}=0$ 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.

6 pages (uses iopart style/class files); (v2) some minor amendments to match published version in Modern Physics Letters A

References in corpus (2)

• Szekeres models: a covariant approach
• Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models

Cited by in corpus (4)

• Symmetry and Equivalence in Szekeres Models
• Quantization of inhomogeneous spacetimes with cosmological constant term
• Quantization of the Szekeres System
• Frame Rotation in the Szekeres Spacetimes