Recently, the existence of gravitational waves has been confirmed in experiments. It is worth then to analyze once again one of the most intriguing open problems of the general theory of relativity: the problem of vacuum type N with twist. It is well known that according to the "peeling off theorem" the graviational radiation far away from a bounded source is of the type N. All vacuum type N...
A new technique is presented in order to build tetrads in four-dimensional Lorentzian spacetimes. These tetrads have special useful properties in general relativity, astrophysics and also particle physics. A new fundamental result is proved in group theory. The group SO(2) (spatial rotations) is isomorphic to the group SO(1; 1) (boosts) plus two kinds of discrete transformations. One of them...
I will review quasi-local aspects of the gravitational field, in particular, energy as a Hamiltonian for the finite region. The considerations are closely related to the initial boundary problem for the gravitational field.
I investigate rotating Bowen-York-type initial data for Einstein equations with a positive cosmological constant. They are obtained using the so-called conformal method. From the technical point of view, its most important part amounts to solving a corresponding Lichnerowicz equation. The first analysis of this equation was recently published by Bizoń, Pletka and Simon. Here I focus on...
Starting from the cyclic models of the parallel universes with different evolution of the fundamental constants and the same geometry I will study the quantum mechanical entanglement problem of the classically separated universes. The basic approach will be based on the third-quantization formalism of quantum cosmology. Some interesting properties of quantum entanglement (entropy and...
It is possible to include unobservable fields and particles in cosmological models (warm inflation of Berera and Moss) as well as contribution of quantum fluctuations (Starobinsky, Vilenkin) by adding a noise term to classical equations. Such a noise term breaks the energy-momentum conservation. I introduce a compensating term to the energy-momentum repairing the conservation laws. Solutions...