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Conditions for smooth cosmological models are set out and applied to inhomogeneous spherically symmetric models constructed by matching together different Lemaitre-Tolman-Bondi solutions to the Einstein field equations. As an illustration…
We present the exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with constant positive density located below $z=0$. This solution depends essentially on two constants: the density…
A family of exact solutions is presented which represents a rigidly rotating cylinder of dust in a background with a negative cosmological constant. The interior of the infinite cylinder is described by the Godel solution. An exact solution…
We investigate non-linear, spherically symmetric solutions to the coupled system of a quintessence field and Einstein gravity. In the presence of a scalar potential, we find regular solutions that to an outside observer very closely…
We solve the Einstein vacuum-equations for the case of static and axisymmetric solutions in a system of coordinates different from the Weyl standard one. We prove that there exists a class of solutions with the appropriate asymptotical…
We study the matching of LRS spatially homogeneous collapsing dust space-times with non-stationary vacuum exteriors in cylindrical symmetry. Given an interior with diagonal metric we prove existence and uniqueness results for the exterior.…
Motivated by studies on gravitational lenses, we present an exact solution of the field equations of general relativity, which is static and spherically symmetric, has no mass but has a non-vanishing spacelike components of the…
We study Einstein's equations with an isotropic but inhomogeneous metric in the cosmic rest frame. The equations are solved perturbatively in the late Universe. The leading plus next-to-leading order results agree with observations without…
We present new exact inhomogeneous vacuum cosmological solutions of Einstein's equations. They provide new information about the nature of general cosmological solutions to Einstein's equations.
We find a new regular solution of six-dimensional Einstein's equations with a positive cosmological constant. It has the same isometry group as the (deformed) conifold geometry, and the superpotential approach is used to solve the equations…
The staid subject of exact static spherically symmetric perfect fluid solutions of Einstein's equations has been reinvigorated in the last decade. We now have several solution generating techniques which give rise to new exact solutions.…
We present a stationary generalization of the static $q-$metric, the simplest generalization of the Schwarzschild solution that contains a quadrupole parameter. It possesses three independent parameters that are related to the mass,…
A new class of higher-dimensional exact solutions of Einstein's vacuum equation is presented. These metrics are written in terms of the exponential of a symmetric matrix and when this matrix is diagonal the solution reduces to…
Einstein equations are addressed with the energy-momentum tensor that appears if the equations under discussion are required to possess conformal invariance. It is proved that thus derived equations (equations of conformally invariant…
We consider the Szekeres universe with an inhomogeneous dust fluid and a homogeneous and isotropic ghost matter source with equation of state $p_{g}=\left( \gamma-1\right) \rho_{g},$ where $\gamma$ is a constant. The field equations…
Higher dimensional, static, cylindrically symmetric vacuum solutions with and without a cosmological constant in the Brans-Dicke theory are presented. We show that, for a negative cosmological constant and for specific values of the…
The static vacuum plane spacetimes are considered, which have two non-trivial solutions: The Taub solution and the Rindler solution. Imposed reflection symmetry, we find that the source for the Taub solution does not satisfy any energy…
In this letter we will revise the steps followed by A. Einstein when he first wrote on cosmology from the point of view of the general theory of relativity. We will argue that his insightful line of thought leading to the introduction of…
We analyse the vacuum static spherically symmetric space-time for a specific class of non-conservative theories of gravity based on the Rastall's theory. We obtain a new vacuum solution which has the same structure as the Schwarzschild-de…
We present a novel homogeneous and geometrically flat exact solution of Einstein's General Relativity equations for an ideal fluid. The solution, which describes an expanding/contracting hypercylinder, fits well with the observational…