Related papers: Non-vacum conformally flat space-times: dark energ…
We present a stationary spherically symmetric solution of the Einstein equations, with a source generated by a scalar field of $q$-theory. In this theory Riemannian gravity, as described by the Einstein - Hilbert action, is coupled to a…
We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…
The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are…
We examine strictly static asymptotically flat spacetimes in Einstein-Gauss-Bonnet gravity with U(1) gauge field, revealing that, up to small curvature corrections, confomally flat slices of the spacetime in question are of Minkowski…
We find a class of exact solutions of differentially rotating dust in the framework of General Relativity. There exist asymptotically flat space-times of the flow with positive mass function that for radii sufficiently large is monotonic…
A class of radiative solutions of Einstein's field equations with a negative cosmological constant and a pure radiation is investigated. The space-times, which generalize the Defrise solution, represent exact gravitational waves which…
We present approximate exterior and interior solutions of Einstein's equations which describe the gravitational field of a static deformed mass distribution. The deformation of the source is taken into account up to the first order in the…
We determine the energy-momentum tensor of non-perfect fluids in thermodynamic equilibrium. To this end, we derive the constitutive equations for energy density, isotropic and anisotropic pressure as well as for heat-flux from the…
To describe the dark side of the Universe, we adopt a novel approach where dark energy is explained as an electrically charged majority of dark matter. Dark energy, as such, does not exist. The Friedmann equation at the present time…
We consider the oscillating dark energy with periodic equation of state in two equivalent formulations: ideal fluid or scalar-tensor theory. It is shown that such dark energy suggests the natural way for the unification of early-time…
A new family of exact solutions of the Einstein field equations for static and axially simmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply written in…
It has been shown that for the Reissner-Nordstrom solution to the vacuum Einstein field equations charge, like mass, has a unique space-time signature [Found. Phys. 38, 293-300 (2008)]. The presence of charge results in a negative…
A solution to Einstein's field equations via the Friedman equations is shown to produce a cosmological model that is in exact agreement with the measurements made by the dark energy astronomers. All the essential physical parameters are…
We present a menagerie of solutions to the vacuum Einstein equations in six, eight and ten dimensions. These solutions describe spacetimes which are either locally asymptotically adS or locally asymptotically flat, and which have…
Five classes of radiative solutions of Einstein's field equations are discussed in the light of some new developments. These are plane waves and their collisions, cylindrical waves, Robinson-Trautman and type N spacetimes, boost-rotation…
Dark energy dynamics of the universe can be achieved by equivalent mathematical descriptions taking into account generalized fluid equations of state in General Relativity, scalar-tensor theories or modified F(R) gravity in Einstein or…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is…
This paper is devoted to the study of matter collineations of plane symmetric spacetimes (for a particular class of spacetimes) when the energy-momentum tensor is non-degenerate. There exists many interesting cases where we obtain proper…
We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the…