The Szekeres metrics with $M < 0$

TL;DR

This paper explores Szekeres metrics with negative mass function, revealing they lack a Big Bang singularity and have negative density, thus not serving as viable cosmological models.

Contribution

It demonstrates the existence of solutions with negative mass in Szekeres metrics and analyzes their properties, including the absence of singularities and shell crossings.

Findings

Solutions with M<0 have no Big Bang singularity.

The density ρ remains negative at all times in these solutions.

Such metrics are not suitable as cosmological models.

Abstract

The evolution equation of the Szekeres metrics allows solutions with the mass function $M < 0$. They exist in both classes of the Szekeres metrics, have no Big Bang singularity and no origin. In both classes, the conditions for no shell crossings ensure that the mass density $\rho$ of the dust source in the Einstein equations is negative at all times. Thus, these metrics do not qualify as cosmological models. In the Friedmann limit, the implication $M < 0 \Longrightarrow \rho < 0$ is immediate. In the general Szekeres metrics it follows through a rather intricate reasoning.