Related papers: The Vacuum Einstein Equations via Holonomy around …
We establish a general gluing theorem for constant mean curvature solutions of the vacuum Einstein constraint equations. This allows one to take connected sums of solutions or to glue a handle (wormhole) onto any given solution. Away from…
We consider self-interacting scalar fields coupled to gravity. Two classes of exact solutions to Einstein's equations are obtained: the first class corresponds to the minimal coupling, the second one to the conformal coupling. One of the…
A closed explicit representation of the vacuum Einstein equations in terms of components of curvature 2-forms is given. The discussion is restricted to the case of non-vanishing cubic invariant of conformal curvature spinor. The complete…
We review spherical and inhomogeneous analytic solutions of the field equations of Einstein and of scalar-tensor gravity, including Brans-Dicke theory, non-minimally (possibly conformally) coupled scalar fields, Horndeski, and beyond…
A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton-Jacobi equation for a test particle is integrated by the method of complete separation of variables with…
We study the Cauchy problem for the Einstein-Boltzmann system with soft potentials in a cosmological setting. We assume the Bianchi I symmetry to describe a spatially homogeneous, but anisotropic universe and consider a cosmological…
Exact solutions to Einstein's equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz)…
The issue of the physical equivalence between the different coordinate system in Einstein theory is revised. Gauge fixing influences results of measurements and physics are different in two different coordinate system. Spacetime metric…
A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime. Since Einstein's equations follow from varying the action, it should be possible to derive them by…
We construct local, in spacetime, singular solutions to the Einstein vacuum equations that exhibit Kasner-like behavior in their past boundary. Our result can be viewed as a localization (in space) of the construction in \cite{FL}. We also…
This article is a guide to the literature on existence theorems for the Einstein equations which also draws attention to open problems in the field. The local in time Cauchy problem, which is relatively well understood, is treated first.…
Smooth Cauchy data for the Einstein-Lambda-vacuum field equations with positive cosmological constant Lambda that are sufficiently close to de Sitter data develop into a solution that admits a smooth conformal boundary Scri+ in its future.…
We classify all spherically symmetric dust solutions of Einstein's equations which are self-similar in the sense that all dimensionless variables depend only upon $z\equiv r/t$. We show that the equations can be reduced to a special case of…
Local solutions are a vivid and long-living topic in gravitational physics. We consider exact static pseudo-spherically symmetric solutions of semi-classical Einstein's equations in presence of the trace anomaly contribution. We investigate…
We study stationary configurations mimicking nonholonomic locally anisotropic black rings (for instance, with ellipsoidal polarizations and/or imbedded into solitonic backgrounds) in three/six dimensional pseudo-Finsler/ Riemannian…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…
According to Birkhoff's theorem the only spherically symmetric solution of the vacuum Einstein field equations is the Schwarzschild solution. Inspite of imposing asymptotically flatness and staticness as initial conditions we obtain that…
We give a sufficient condition, with no restrictions on the mean curvature, under which the conformal method can be used to generate solutions of the vacuum Einstein constraint equations on compact manifolds. The condition requires a…
We consider four-dimensional Einstein gravity minimally coupled to a dilaton scalar field with a supergravity-inspired scalar potential. We obtain an exact time-dependent spherically symmetric solution describing gravitational collapse to a…