Related papers: Exact Solutions for Compact Objects in General Rel…
We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by…
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…
Interior solutions of Einstein's equations with a non-zero cosmological constant are given for static and spherically symmetric configurations of uniform density. The metric tensor and pressure are determined for both positive and negative…
We demonstrate a technique to generate new class of exact solutions to the Einstein-Maxwell system describing a static spherically symmetric relativistic star with anisotropic matter distribution. An interesting feature of the new class of…
We find a set of spacetime solutions whose rotation curves approach a flat profile at large radii, as observed for spiral galaxies. The associated stress-energy tensor reflects a positive mass and anisotropic pressure. The spatially…
A procedure to find static axially symmetric solutions to the Einstein field equations is presented. We obtained two general solutions and five particular solutions, which depend on the existence conditions for circular and $z$ direction…
Einstein's spherically symmetric interior gravitational equations are investigated. Following Synge's procedure, the most general solution of the equations is furnished in case $T^{1}_{1}$ and $T^{4}_{4}$ are prescribed. The existence of a…
Numerical solutions to the Einstein constraint equations are constructed on a selection of compact orientable three-dimensional manifolds with non-trivial topologies. A simple constant mean curvature solution and a somewhat more complicated…
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…
In this work, we examine a spherically symmetric compact body with isotropic pressure profile, in this context we obtain a new class of exact solutions of Einstein's-Maxwell field equation for compact stars with uniform charged…
The Einstein-Maxwell equations with anisotropic pressures and electromagnetic field are studied with a polytropic equation of state. New exact solutions to the field equations are generated in terms of elementary functions. Special cases of…
In this paper, we investigate the anisotropic interior spherically symmetric solutions by utilizing the extended gravitational decoupling method in the background of $f(G,T)$ gravity, where $G$ and $T$ signify the Gauss-Bonnet term and…
We prove the local existence of solutions to the Einstein-Elastic equations that represent self-gravitating, relativistic elastic bodies with compact support.
In the context of linear $f(\mathcal{R},T)=\mathcal{R}+\chi T$ gravity, where $\mathcal{R}$ is the Ricci scalar, $T$ is the trace of the energy-momentum tensor, and $\chi$ is a dimensionless parameter, we have obtained exact analytical and…
We study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres are composed of a perfect fluid with a charge distribution that creates a…
We show that equations of Newtonian hydrodynamics and gravity with Einstein's cosmological constant included admit gravitostatic wave solutions propagating in the background of Einstein's static Universe. In the zero pressure limit these…
The trace-free Einstein equations contain one equation less than the complete field equations. In a static and spherically symmetric spacetime, the number of field equations is thus reduced to two. The equation of pressure isotropy of…
It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "open" model $H^ 3$ for this…
We find a reconstruction algorithm able to generate all the static spherically symmetric interior solutions in the framework of Ho\v{r}ava gravity and Einstein-\ae ther theory in presence of anisotropic fluids. We focus for simplicity on…
Recently, a family of exact force-free electrodynamic (FFE) solutions was given by Brennan, Gralla and Jacobson, which generalizes earlier solutions by Michel, Menon and Dermer, and other authors. These solutions have been proposed as…