Related papers: Vacuum solutions which cannot be written in diagon…
The gravitational field equations in general relativity (GR) consist of a sophisticated system of nonlinear partial differential equations. Solving such equations in some generic off-diagonal forms is usually a hard analytic or numeric…
Astrophysical black holes arise as exact solutions of the Einstein field equations. Therefore, any alternative, such as a gravastar, must satisfy the same level of mathematical rigor and internal consistency. A physically viable gravastar…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
Since Schwarzshild discovered the point-mass solution to Einstein's equations that bears his name, many equivalent forms of the metric have been catalogued. Using an elementary coordinate transformation, we derive the most general form for…
Generalized Dirac equation containing vacuum-mass contribution is introduced. The vacuum-mass contribution arises due to the coupling of quantum mechanical matter field with the vacuum field. Vacuum stress energy tensor arises in the…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
In this work, we construct a modified version of the Einstein field equations for a vacuum and spherically symmetric spacetime in terms of the Riemann-Louville fractional derivative. The main difference between our approach and other works…
The Einstein field equations for a class of irrotational non-orthogonally transitive $G_{2}$ cosmologies are written down as a system of partial differential equations. The equilibrium points are self-similar and can be written as a…
The quantum field theoretic prediction for the vacuum energy density leads to a value for the effective cosmological constant that is incorrect by between 60 to 120 orders of magnitude. We review an old proposal of replacing Einstein's…
The generalized Maxwell equations are considered which include an additional gradient term. Such equations describe massless particles possessing spins one and zero. We find and investigate the matrix formulation of the first order of…
A d-dimensional spacetime is "axisymmetric" if it possesses an SO(d-2) isometry group whose orbits are (d-3)-spheres. In this paper, algebraically special, axisymmetric solutions of the higher dimensional vacuum Einstein equation (with…
A method of solving the Einstein equations with a scalar field is presented. It is applied to find higher dimensional vacuum metrics invariant under the group SO(n + 1) acting on n-dimensional spheres.
The algebra and calculus of generalized differential forms are reviewed and employed to construct a class of generalized connections and to investigate their properties. The class includes generalized connections which are flat when…
In this paper attention is focused on gravitational sector of the Born--Infeld theory, suggested in quant-ph/9608014. Vacuum equations for gravitational field are derived. The asymptotic for modified Schwarzschild solution is obtained, as a…
In the present article we find a new class of solutions of Einstein's field equations. It describes stationary, cylindrically symmetric spacetimes with closed timelike geodesics everywhere outside the symmetry axis. These spacetimes contain…
A non-static solution of Einstein's field equations of General Relativity representing the gravitational field of an axisymmetric radiation flow is obtained using the Eddington or the Kerr-Schild form for the metric. A solution obtained…
The exact axisymmetric and static solution of the Einstein equations coupled to axisymmetric and static gravitating scalar (or phantom) field is presented. The spacetimes modified by the scalar field are explicitly given for the so called…
We present the exact solution to the linearized Maxwell equations in space-time slightly curved by a gravitational wave. We show that in general, even dealing with a first-order theory in the strength of the gravitational field, the…
We consider the Einstein-Dirac field equations describing a self-gravitating massive neutrino, looking for axially-symmetric exact solutions; in the search of general solutions, we find some that are specific and which have critical…
In contrast to the phenomenon of nullification of the cosmological constant in the equilibrium vacuum, which is the general property of any quantum vacuum, there are many options in modifying the Einstein equation to allow the cosmological…