Hyperbolically symmetric versions of Lemaitre-Tolman-Bondi spacetimes

TL;DR

This paper explores hyperbolically symmetric fluid solutions in general relativity, extending LTB models to hyperbolic symmetry, and finds specific conditions under which solutions are non-dissipative and have zero complexity.

Contribution

It introduces hyperbolically symmetric versions of LTB spacetimes, analyzing their properties and conditions for vanishing complexity in dissipative and non-dissipative cases.

Findings

Pure dust models have non-zero complexity factor.

Vanishing complexity models are non-dissipative with stiff equation of state.

Solutions with zero complexity are hyperbolically symmetric, non-dissipative, and stiff.

Abstract

We study fluid distributions endowed with hyperbolical symmetry, which share many common features with Lemaitre-Tolman-Bondi (LTB) solutions (e.g. they are geodesic, shearing, non--conformally flat and the energy density is inhomogeneous). As such they may be considered as hyperbolically symmetric versions of LTB, with spherical symmetry replaced by hyperbolical symmetry. We start by considering pure dust models, and afterwards we extend our analysis to dissipative models with anisotropic pressure. In the former case the complexity factor is necessarily non-vanishing, whereas in the latter cases models with vanishing complexity factor are found. The remarkable fact is that all solutions satisfying the vanishing complexity condition are necessarily non-dissipative and satisfy the stiff equation of state.