The Szekeres metrics with $M < 0$

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.