A central aim of this book is to show that there is much still to be learned about the evolution and effects of exact nonlinear inhomogeneities in Einstein's theory, and that this is highly relevant to the real Universe.

The Universe as we observe it is very inhomogeneous. Among its structures there are groups and clusters of galaxies, large cosmic voids and very large elongated structures such as filaments and walls. In cosmology, however, the homogeneous and isotropic models of the Robertson–Walker class have been used almost exclusively, and in these, structure formation is described by an approximate perturbation theory. This works well as long as the perturbations remain small, but cannot be applied once perturbations become large and evolution becomes nonlinear. This is where the methods of inhomogeneous cosmology must come into play. These methods can be employed not only to study the evolution of cosmic structures, but also to investigate the formation and evolution of black holes, as well as studying the geometry and dynamics of the Universe.

Whatever the successes of the Concordance model, based on an FLRW metric plus perturbation theory, structure evolution does sooner or later become nonlinear and non-Newtonian, and our understanding of present-day observations will be incomplete without the methods of inhomogeneous cosmology. The phenomena of fully relativistic inhomogeneous evolution must occur and cannot be ignored.

This book presents the application of inhomogeneous exact solutions of the Einstein equations in such areas as the evolution of galactic black holes and cosmic structures, and the impact of inhomogeneities on light propagation which allows us to solve the horizon and dark energy problems.