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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…
Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid…
We present a method for constructing stationary, asymptotically flat, rotating solutions of Einstein's field equations. One of the spun-up solutions has quasilocal mass but no global mass. It has an ergosphere but no event horizon. The…
Recently, it has been suggested that the phenomenology of flat rotation curves observed at large radii in the equatorial plane of disk galaxies can be explained as a manifestation of General Relativity instead of the effect of Dark Matter…
Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantised gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically…
This article belongs to a series where the influence of anisotropic pressure on the gravitational properties of rigidly rotating fluids is studied using new exactsolutions of GR constructed for the purpose. For mathematical simplification,…
We study generic Einstein-Maxwell-Kalb-Ramond-dilaton actions, and derive conditions under which they give rise to static, spherically symmetric black hole solutions. We obtain new asymptotically flat and non-flat black hole solutions which…
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…
We study slowly rotating, asymptotically flat black holes in Einstein-aether theory and show that solutions that are free from naked finite area singularities form a two-parameter family. These parameters can be thought of as the mass and…
We derive the equations governing static, spherically symmetric vacuum solutions to the Einstein equations, as modified by the frame-dependent effective action arising from trace dynamics. We give analytic and numerical results for the…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…
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…
We introduce a new type of generating theorems in General Relativity for anisotropic, static, spherically symmetric solutions of the Einstein field equations. The results are used to derive a class of solutions that can serve as new models…
How do the global properties of a Lorentzian manifold change when endowed with a vector field? This interesting question is tackled in this paper within the framework of Einstein-Aether (EA) theory which has the most general…
We present stationary and axially-symmetric black hole solutions to the Einstein field equations sourced by an anisotropic fluid, describing rotating black holes embedded in astrophysical environments. We compute their physical properties,…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
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…
The requirements are formulated which lead to the existence of the class of globally regular solutions to the minimally coupled GR equations which are asymptotically de Sitter at the center. The brief review of the resulting geometry is…
New general spherically symmetric solutions have been derived with a cosmological "constant" \Lambda as a source. This \Lambda field is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed…
We derive an asymptotic solution of the vacuum Einstein equations that describes the propagation and diffraction of a localized, large-amplitude, rapidly-varying gravitational wave. We compare and contrast the resulting theory of strongly…