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A number of recent observations have suggested that the Einstein's theory of general relativity may not be the ultimate theory of gravity. The f(R) gravity model with R being the scalar curvature turns out to be one of the best bet to…
In this paper we will make a survey of solutions to the Wheeler-Dewitt equation which have been found up to now in Ashtekar's formulation for canonical quantum gravity. Roughly speaking they are classified into two categories, namely,…
We investigate the static and spherically symmetric solutions in a class of the generalized Proca theory with the nonminimal coupling to the Einstein tensor. First, we show that the solutions in the scalar-tensor theory with the nonminimal…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
We demonstrate that the generic charged rotating regular black hole solutions of general relativity coupled to non-linear electrodynamics, obtained by using the alternate Newman-Janis algorithm, introduces only small (on level $10^{-2}$)…
We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing…
We construct explicitly deformations of Einstein's theory of gravity that are consistent and phenomenologically viable since they respect, in particular, cosmological backgrounds. We show that these deformations have unique symmetries in…
Einstein-Dirac equations for two spinor fields are considered. It is shown that in this case one can obtain self-consistent equations set for these gravitating spinors. The key idea to obtain Einstein-Dirac equations is to use special…
Einstein gravity minimally coupled to a self-interacting scalar field is investigated in the static and isotropic situation. We explicitly construct in partially closed form a new black-hole solution with exponentially decaying scalar hair.…
Regular bouncing solutions in the framework of a scalar-tensor gravity model were found in a recent work. We reconsider the problem in the Einstein frame (EF) in the present work. Singularities arising at the limit of physical viability of…
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…
In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the…
We construct globally regular gravitating solutions, which possess only discrete symmetries. These solutions of Yang-Mills-dilaton theory may be viewed as exact (numerical) solutions of scalar gravity, by considering the dilaton as a kind…
The solutions of $U(1)$ gauge-gravity coupling is one of the interesting models for analyzing the semi-classical nature of spacetime. In this regard, different well-known singular and nonsingular solutions have been taken into account. The…
General relativity has two fundamental problems that render it unsuitable for tackling the gravitational field's quantization. The first problem is the lack of a genuine gravitational variable representing gravitation only, inertial forces…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
Three non-existence results are established for self-gravitating solitons in Einstein-Maxwell-scalar models, wherein the scalar field is, generically, non-minimally coupled to the Maxwell field via a scalar function $f(\Phi)$. Firstly, a…
De Sitter solutions play an important role in cosmology because the knowledge of unstable de Sitter solutions can be useful to describe inflation, whereas stable de Sitter solutions are often used in models of late-time acceleration of the…
A scalar theory of gravity extending Newtonian gravity to include field energy as its source is developed. The physical implications of the theory are probed through its spherically symmetric (source) solutions. The aim is to demonstrate…
Starting with the 2+1 Einstein--Maxwell--Dilaton system with a cosmological constant and assuming two commuting Killing symmetries we derive the corresponding $1+0 \sigma$--model. It is shown that, for general values of the coupling…