[en] 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 Lemaitre-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.

[en] It was shown recently that the SU(2) sigma model coupled to gravity has periodic spherically symmetric self-similar solutions for small values of the coupling constant. In this article we extend the analysis of Bizon, Szybka, and Wasserman to larger values of the coupling constant (α≥0.426) and present numerical evidence for the chaotic solution and the fractal threshold behavior. We explain this phenomenon in terms of horseshoelike dynamics and heteroclinic intersections

[en] We continue our studies of spherically symmetric self-similar solutions in the SU(2) sigma model coupled to gravity. Using mixed numerical and analytical methods we show the existence of an unstable periodic solution lying at the boundary between the basins of two generic attractors

[en] We show that analytic solutions E of the Ernst equation with a non-empty zero-level set of RE lead to smooth ergosurfaces in spacetime. In fact, the spacetime metric is smooth near an 'Ernst ergosurface' E_f if, and only if, E is smooth near E_f and does not have zeros of infinite order there

[en] We study the effect of small-scale inhomogeneities for Einstein clusters. We construct a spherically symmetric static spacetime with small-scale radial inhomogeneities and propose the Gedankenexperiment. An hypothetical observer at the center constructs, using limited observational knowledge, a simplified homogeneous model of the configuration. An idealization introduces side effects. The inhomogeneous spacetime and the effective homogeneous spacetime are given by simple solutions to Einstein equations. They provide a basic toy-model for studies of the effect of small-scale inhomogeneities in general relativity. We show that within our highly inhomogeneous model the effect of small-scale inhomogeneities remains small for a central observer. The homogeneous model fits very well to all hypothetical observations as long as their precision is not high enough to reveal a tension.

[en] We prove uniqueness of the near-horizon geometries arising from degenerate Kerr black holes within the collection of nearby vacuum near-horizon geometries. (paper)

[en] 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. (paper)

[en] 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, \ie 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