Ghosts in a Mirror

Abstract

We look at some dynamic geometries produced by scalar fields with both the "right" and the "wrong" sign of the kinetic energy. We start with anisotropic homogeneous universes with closed, open and flat spatial sections. A non-singular solution to the Einstein field equations representing an open anisotropic universe with the ghost field is found. This universe starts collapsing from $t \to -\infty$ and then expands to $t \to \infty$ without encountering singularities on its way. We further generalize these solutions to those describing inhomogeneous evolution of the ghost fields. Some interesting solutions with the plane symmetry are discussed. These have a property that the same line element solves the Einstein field equations in two mirror regions $|t|\geq z$ and $|t|\leq z$, but in one region the solution has the \emph{right} and in the other, the \emph{wrong} signs of the kinetic energy. We argue, however, that a physical observer can not reach the mirror region in a finite proper time. Self-similar collapse/expansion of these fields are also briefly discussed.