Abstract. We construct the first exact statistically homogeneous and isotropic cosmological solution in which inhomogeneity has a significant effect on the expansion rate. The universe is modelled as a Swiss Cheese, with dust FRW background and inhomogeneous holes. We show that if the holes are described by the quasispherical Szekeres solution, their average expansion rate is close to the background under certain rather general conditions. We specialise to spherically symmetric holes and violate one of these conditions. As a result, the average expansion rate at late times grows relative to the background, i.e. backreaction is significant. The holes fit smoothly into the background, but are larger on the inside than a corresponding background domain: we call them Tardis regions. We study light propagation, find the effective equations of state and consider the relation of the spatially averaged expansion rate to the redshift and the angular diameter distance.

We introduce a new class of two-dimensional diagrams, the \emph{projection diagrams}, as a tool to visualize the global structure of space-times. We construct the diagrams for several metrics of interest, including the Kerr-Newman - (anti) de Sitter family, with or without cosmological constant, and the Emparan-Reall black rings.Comment: 41 pages, minor changes and correction

We study the effect of inhomogeneities on light propagation. The Sachs equations are solved numerically in the Swiss-cheese models with inhomogeneities modeled by the Lemaître-Tolman solutions. Our results imply that, within the models we study, inhomogeneities may partially mimic the accelerated expansion of the Universe provided the light propagates through regions with lower than the average density. The effect of inhomogeneities is small and full randomization of the photons' trajectories reduces it to an insignificant level.

Abstract:We prove smoothness of the domain of outer communications (d.o.c.) of the Black Saturn solutions of Elvang and Figueras. We show that the metric on the d.o.c. extends smoothly across two disjoint event horizons with topology R × S 3 and R × S 1 × S 2 . We establish stable causality of the d.o.c. when the Komar angular momentum of the spherical component of the horizon vanishes, and present numerical evidence for stable causality in general.

We show that the angular momentum -area inequality 8π|J| ≤ A for weakly stable minimal surfaces would apply to I + -regular many-Kerr solutions, if any existed. Hence we remove the undesirable hypothesis in the Hennig-Neugebauer proof of non-existence of well behaved two-component solutions.