Cylindrically symmetric dust spacetime

TL;DR

This paper presents an exact solution to Einstein's equations describing an inhomogeneous, cylindrically symmetric dust universe that expands and recollapses, revealing surprising features like non-simultaneous big-bang and big-crunch singularities, and potential instability of flat spacetime.

Contribution

It introduces a new explicit inhomogeneous dust spacetime with cylindrical symmetry, showing novel features and implications for spacetime stability.

Findings

Universe has non-simultaneous big-bang and big-crunch singularities.

Part of the big-crunch singularity is naked.

Spacetime can be a small perturbation of Minkowski space.

Abstract

We present an explicit exact solution of Einstein's equations for an inhomogeneous dust universe with cylindrical symmetry. The spacetime is extremely simple but nonetheless it has new surprising features. The universe is ``closed'' in the sense that the dust expands from a big-bang singularity but recollapses to a big-crunch singularity. In fact, both singularities are connected so that the whole spacetime is ``enclosed'' within a single singularity of general character. The big-bang is not simultaneous for the dust, and in fact the age of the universe as measured by the dust particles depends on the spatial position, an effect due to the inhomogeneity, and their total lifetime has no non-zero lower limit. Part of the big-crunch singularity is naked. The metric depends on a parameter and contains flat spacetime as a non-singular particular case. For appropriate values of the parameter the spacetime is a small perturbation of Minkowski spacetime. This seems to indicate that flat spacetime may be unstable against some global {\it non-vacuum} perturbations.