Approaching Wonderland

Abstract

Continuing previous work, we show the existence of stable, anisotropic future attractors in Bianchi invariant sets with a $p$-form field ($p\,\in\,\{1,3\}$) and a perfect fluid. In particular, we consider the not previously investigated Bianchi invariant sets $\mathcal{B}$(II), $\mathcal{B}$(IV), $\mathcal{B}$(VII$_0$) and $\mathcal{B}$(VII$_{h})$ and examine their asymptotic behaviour. We find that the isolated equilibrium set Wonderland is a future attractor on all of its existence ($2/3<\,\gamma\,<2$) in all these sets except in $\mathcal{B}$(II), where the peculiar equilibrium sets Edge and Rope show up, taking over the stability for certain values of $\gamma$. In addition, in $\mathcal{B}$(IV) and $\mathcal{B}$(VII$_h$) plane gravitational wave solutions (with a non-zero $p$-form) serve as attractors whenever $2/3<\,\gamma\,<2$.