Related papers: Quadrupolar metrics
The exact solution to the Einstein equations that represents a static axially symmetric source deformed by an internal quadrupole is considered. By using the Poincare section method we numerically study the geodesic motion of test…
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
Under a weak assumption of the existence of a geodesic null congruence, we present the general solution of the Einstein field equations in three dimensions with any value of the cosmological constant, admitting an aligned null matter field,…
We examine static perfect fluid spheres in the presence of a cosmological constant. New exact matter solutions are discussed which require the Nariai metric in the vacuum region. We generalize the Einstein static universe such that neither…
In the present paper we have constructed a new relativistic anisotropic compact star model having a spherically symmetric metric of embedding class one. Here we have assumed an arbitrary form of metric function and solved the Einstein…
On a spacetime $(M,g)$ endowed with a density function $h$, we consider the vacuum weighted Einstein field equations: \[h\rho-\operatorname{Hes}_h+\Delta h g=0.\] First, it is shown that the equation characterizes critical metrics for an…
We consider $d$-dimensional static spacetimes in Einstein gravity with a cosmological constant in the presence of a minimally coupled massless scalar field. The spacetimes have a $(d-2)$-dimensional base manifold given by an Einstein space…
We derive the general solution to the coupled Einstein and Dirac field equations in static and hyperplane-symmetric spacetime of arbitrary dimension including a cosmological constant of either sign. As a result, only a massful Dirac field…
We propose a new numerical method to calculate irrotational binary systems composed of compressible gaseous stars in Newtonian gravity. Assuming irrotationality, i.e. vanishing of the vorticity vector everywhere in the star in the inertial…
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…
In this work, we provide a novel exact solution to the Einstein-Maxwell field equations in isotropic coordinates for charged anisotropic matter distribution, achieved by considering one of the metric potentials as well as a particular form…
We show quantitatively that an exact solution of Einstein's conformal gravity can explain very well the galactic rotation curves for a sample of 104 galaxies without need for dark matter or other exotic modification of gravity. The metric…
These notes address the planar gravitational wave solutions of general relativity in empty space-time, and analyze the motion of test particles in the gravitational wave field. Next we consider related solutions of the Einstein equations…
A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…
When describing gravity at high energies it is natural to introduce terms quadratic in the curvature as first corrections to the Einstein-Hilbert action. Static, spherically symmetric classical solutions are studied in the case of the…
We provide exact solutions to the Einstein equations when the Universe contains vacuum energy plus a uniform arrangements of magnetic fields, strings, or domain walls. Such a universe has planar symmetry, i. e., it is homogeneous but, not…
Solving the classical equations of motion in general relativity recursively, we consider the metric of a spatially localized and stationary source of matter. Having in mind a star of general composition, we characterize it by means of its…
The main goal of this work is to provide a comprehensive study of relativistic structures in the context of recently proposed {$\mathcal{R}+ \alpha \mathcal{A}$} gravity, where $\mathcal{R}$ is the Ricci scalar, and $\mathcal{A}$ is the…
In this paper we employ numerical methods to study the Einstein equation \[ Ric(g)=\lambda\, g, \] where $Ric$ is the Ricci tensor and $\lambda$ is the Einstein constant, restricted to a class of full flag manifolds. These metrics describe…