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In this paper we study the solutions of different forms of fractional equations on the unit sphere $\mathbb{S}_{1}^{2}$ $\subset \mathbb{R}^{3}$ possessing the structure of time-dependent random fields. We study the correlation functions of…
A higher order theory of gravitation is considered which is obtained by modifying Einstein field equations. The Lagrange used to modify this in the form a polynomial in (scalar curvature) R. In this equation we have studied spherical…
The string model of gravitational force is proposed where the string forms the mediation of the gravitational interaction between two gravitating bodies. It reproduces the Newtonian results in the first-order approximation and it predicts…
This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…
We discuss static, cylindrically symmetric vacuum solutions of hybrid metric-Palatini gravity (HMPG), a recently proposed theory that has been shown to successfully pass the local observational tests and to produce a certain progress in…
In this work we present an approximate solution of the Einstein equations describing a global model for the gravitational field generated by a bounded, self-gravitating stationary and axisymmetric body rotating rigidly with constant angular…
The black hole solutions to Einstein's vacuum field equations are also solutions to the equations of motion of the low energy limit of superstring theory. At the same time, string theory boasts a much broader and richer collection of black…
Using a continued fraction ansatz we obtain an analytic approximation for a spherically symmetric black hole solution to Einsteinian Quartic Gravity (EQG), the next simplest Generalized Quasi-Topological Gravity (GQTG) after Einsteinian…
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…
Recently, an approximated solution of the Einstein equations for a rotating body whose mass effects are negligible with respect to the rotational ones has been derived by Tartaglia. At first sight, it seems to be interesting because both…
We find exact solutions of the Einstein equations which describe a black hole pierced by infinitely thin cosmic strings. The string segments enter the black hole along the radii and their positions coincide with the symmetry axes of a…
Solutions of Einstein's equations are found for global defects in a higher-dimensional spacetime with a nonzero cosmological constant Lambda. The defect has a (p-1)-dimensional core (brane) and a `hedgehog' scalar field configuration in the…
According to general relativity, black holes are incomplete, which prevents developing a complete physical description of their dynamical formation and evolution once quantum effects are taken into account. Theories beyond general…
In axial symmetry, there is a gauge for Einstein equations such that the total mass of the spacetime can be written as a conserved, positive definite, integral on the spacelike slices. This property is expected to play an important role in…
We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…
We study the properties of a system consisting of an uncharged spherically symmetric two dimensional extended object which encloses a stationary point charge placed in the shell's center. We show that there can be a static and stable…
According to Einstein's mass-energy equivalence, a body with a given mass extending in a large region of space, will get a smaller mass when confined into a smaller region, because of its own gravitational energy. The classical self-energy…
The main objective of this work is the construction of regular black hole solutions in the context of the Einstein-Maxwell theory. The strategy is to match an interior regular solution to an exterior electrovacuum solution. With this…
Two types of non-Hermitian systems are considered. One of them is both non-Hermitian and non-Linear and an iterative process is used to obtain excited state solutions; the ground state may be solved exactly. The model has been used in many…
A new exact solution of the Einstein-Maxwell equations for the gravitational collapse of a shell of matter in an already formed black hole is given. Both the shell and the black hole are endowed with electromagnetic structure and are…