Related papers: Vacuum solutions which cannot be written in diagon…
The gravitational field of an idealized plane-wave solution of the Maxwell equations can be described in closed form. After discussing this particular solution of the Einstein-Maxwell equations, the motion of neutral test particles, which…
We obtain the most general solution of the Einstein electro - vacuum equation for the stationary axially symmetric spacetime in which the Hamilton-Jacobi and Klein - Gordon equations are separable. The most remarkable feature of the…
By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to the electromagnetic theory. It turns out that the duality symmetry of the Einstein action…
In this note we prove that quantum gravitational corrections to vacuum solutions of Einstein's equations vanish at second order in curvature.
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a…
We analyze a class of topological static spherically symmetric vacuum solutions in $f(Q)$-gravity. We considered an Ansatz ensuring that those solutions trivially satisfy the field equations of the theory when the non-metricity scalar is…
In this article we study self-gravitating static solutions of the Einstein-ScalarField system in arbitrary dimensions. We discuss the existence and the non-existence of geodesically complete solutions depending on the form of the scalar…
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…
Here we describe a stationary cylindrically symmetric solution of Einstein's equation with matter consisting of a positive cosmological and rotating dust term. The solution approaches Einstein static universe solution.
Several exact, cylindrically symmetric solutions to Einstein's vacuum equations are given. These solutions were found using the connection between Yang-Mills theory and general relativity. Taking known solutions of the Yang-Mills equations…
A new approximate solution of vacuum and stationary Einstein field equations is obtained. This solution is constructed by means of a power series expansion of the Ernst potential in terms of two independent and dimensionless parameters…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
We study the exact solution of Einstein's field equations consisting of a ($n+2$)-dimensional static and hyperplane symmetric thick slice of matter, with constant and positive energy density $\rho$ and thickness $d$, surrounded by two…
Starting from a spherically symmetric tetrad with three unknown functions of the radial coordinate, a general solution of M{\o}ller's field equations in case of spherical symmetry nonsingular black hole is derived. The previously obtained…
We show that the Schwarzschild solution can be embedded in a class of nonstandard solutions of the vacuum Einstein's equations with arbitrary rotation curves. These nonstandard solutions have to be taken as physical if dark matter as needed…
The Einstein equations for static gravitational field depend on energy density and pressure. So one may expect that solutions should depend on two parameters: mass and its analogue originated from pressure. Yet the Schwarzschild solution…
When solving the Einstein's equations for an isolated system of masses, V. Fock introduces harmonic reference frame and obtains an unambiguous solution. Further, he concludes that there exists a harmonic reference frame which is determined…
We report on a new solution to the Einstein-Maxwell equations in 2+1 dimensions with a negative cosmological constant. The solution is static, rotationally symmetric and has a non-zero magnetic field. The solution can be interpreted as a…
Using the Euclidon method, a stationary solution of Einstein's vacuum equations was obtained, describing N rotating axially symmetric masses, which in the absence of rotation describes N arbitrary axially symmetric static masses, for…
We investigate the vacuum and charged spherically symmetric static solutions of the Einstein equations on cosmological background. The background metric is not flat, but curved, with constant - curvature spatial sections. Both vacuum and…