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We utilize the gravitational decoupling via the extended geometric deformation to extend the Schwarzschild vacuum solution to new black holes in Rastall theory. By employing linear transformations that deform both the temporal and radial…
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…
Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…
Gravitational decoupling allows to obtain new solutions of general relativity. In this paper, we obtain new solutions of the Einstein field equations which describe non-singular black holes. We consider Hayward and Bardeen regular black…
When solving the equations of General Relativity in a symmetric sector, it is natural to consider the same symmetry for the geometry and stress-energy. This implies that for static and isotropic spacetimes, the most general natural…
Einstein's theory of general relativity predicts that the only stationary configuration of an isolated black hole is the Kerr spacetime, which has a unique multipolar structure and a spherical shape when non-spinning. This is in striking…
We provide a new class of interior solutions for anisotropic stars admitting conformal motion. The Einstein's field equations in this construction are solved for specific choices of the density/mass functions. We analyze the behavior of the…
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…
This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been…
We model a compact relativistic body with anisotropic pressures in the presence of an electric field. The equation of state is barotropic with a linear relationship between the radial pressure and the energy density. Simple exact models of…
By applying the method of moving frames modelling one and two dimensional local anisotropies we construct new solutions of Einstein equations on pseudo-Riemannian spacetimes. The first class of solutions describes non-trivial deformations…
The intimate relations between Einstein's equation, conformal geometry, geometric asymptotics, and the idea of an isolated system in general relativity have been pointed out by Penrose many years ago. A detailed analysis of the interplay of…
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…
We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter…
We analyze the applications of general relativity in relativistic astrophysics in order to solve the problem of describing the geometric and physical properties of the interior and exterior gravitational and electromagnetic fields of…
In the present article a new class of exact solutions of Einstein's field equations for charged anisotropic distribution is obtained on the background of pseudo-spheroidal spacetime characterized by the metric potential…
We investigate anisotropic cosmological solutions of the theory with non-minimal couplings between electromagnetic fields and gravity in $Y(R) F^2$ form. After we derive the field equations by the variational principle, we look for…
We find two new classes of exact solutions to the Einstein-Maxwell system of equations. The matter distribution satisfies a linear equation of state consistent with quark matter. The field equations are integrated by specifying forms for…
For an infinitesimal deformation of a Riemannian manifold, we prove that the scalar, vector, and tensor modes in decompositions of perturbations of the metric tensor, the scalar curvature, the Ricci tensor, and the Einstein tensor decouple…
We study some exact and approximate solutions of Einstein's equations that can be used to describe the gravitational field of astrophysical compact objects in the limiting case of slow rotation and slight deformation. First, we show that…