Final fate of Kantowski–Sachs gravitational collapse

Although it is not a fundamental question, determining exact and general solutions for a given theory has advantages over a numerical integration in many specific cases. Of course, respecting the peculiarities of the problem. Revisiting the integration of the General Relativity Theory field equations for the Kantowski–Sachs spacetime describes a homogeneous but anisotropic universe whose spatial section has the topology of [Formula: see text], we integrate the equations for arbitrary curvature parameter and write the solutions considering the process of gravitational collapse. We took the opportunity and made some comments involving some features of the model such as energy density, shear, viscosity and the production of gravitational waves via Petrov classification.

Wave-like spatially homogeneous models of Stackel spacetimes (3.1) type in the scalar-tensor theory of gravity

All classes of spatially homogeneous spacetime models in the generalized scalar–tensor theory of gravitation are found to allow the integration of the equations of motion of test particles and the eikonal equation by the method of separation of variables by type (3.1). Three classes of exact solutions are obtained that relate to Shapovalov wave-like spacetime models. The resulting spacetime models are of types IV, VI and VII according to the Bianchi classification and type N according to Petrov classification.

Unification of dark energy and dark matter based on the Petrov classification and space-time symmetry

The Petrov classification of stress-energy tensors provides a model-independent definition of a vacuum by the algebraic structure of its stress-energy tensor and implies the existence of vacua whose symmetry is reduced as compared with the maximally symmetric de Sitter vacuum associated with the Einstein cosmological term. This allows to describe a vacuum in general setting by dynamical vacuum dark fluid, presented by a variable cosmological term with the reduced symmetry which makes vacuum dark fluid essentially anisotropic and allows it to be evolving and clustering. The relevant regular solutions to the Einstein equations describe regular cosmological models with time-evolving and spatially inhomogeneous vacuum dark energy, and compact vacuum objects generically related to a dark energy through the de Sitter vacuum interior: regular black holes, their remnants and self-gravitating vacuum solitons — which can be responsible for observational effects typically related to a dark matter. The mass of objects with de Sitter interior is generically related to vacuum dark energy and to breaking of space-time symmetry.

Axially Symmetric, Asymptotically Flat Vacuum Metric with a Naked Singularity and Closed Timelike Curves

We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity. The space-time is regular everywhere except on the symmetry axis where it possesses a true curvature singularity. The space-time is of type D in the Petrov classification scheme and is locally isometric to the metrics of case IV in the Kinnersley classification of type D vacuum metrics. Additionally, the space-time also shows the evolution of closed timelike curves (CTCs) from an initial hypersurface free from CTCs.