Related papers: Einstein manifolds in Ashtekar variables: explicit…
Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in the vacuum case. In this article, to gain a clearer…
It is shown that the vacuum Einstein equations for an arbitrary stationary axisymmetric space-time can be completely separated by re-formulating the Ernst equation and its associated linear system in terms of a non-autonomous…
We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally…
In this paper, the radiation field is defined for solutions to Einstein vacuum equations which are close to Minkowski space-time with spacial dimension $n\geq 4$. The regularity properties and asymptotic behavior of those Einstein vacuum…
We present exact solutions in Einstein-aether theory in a static spherically symmetric background space with a spacelike aether field, as a difference with the usual selection of timelike aether field. We assume a coupling between the…
All Lorentz invariant solutions of vacuum Einstein's equations are found. It is proved that these solutions describe space-times of constant curvature.
We derive a new class of exact solutions characterized by the Szekeres-Szafron metrics (of class I), admitting in general no isometries. The source is a fluid with viscosity but zero heat flux (adiabatic but irreversible evolution) whose…
In this paper we propose a class of exact solutions (stationary and non-stationary) of Einstein's field equations. The energy-momentum tensors of the solutions describe dark energy.
We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with an apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to…
We construct exact static inhomogeneous solutions to Einstein's equations with counter flow of particle fluid and a positive cosmological constant by using the Sasaki metrics on three-dimensional spaces. The solutions, which admit an…
We study solutions to the static vacuum Einstein equations on exterior domains with prescribed metric and mean curvature on the inner boundary. It is proved that for any such boundary data near the standard round boundary data in Euclidean…
We reconsider the large $N$ asymptotics of Harish-Chandra-Itzykson-Zuber integrals. We provide, using Dyson's Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary…
We present a method for generating exact solutions of Einstein equations in vacuum using harmonic maps, when the spacetime possesses two commutating Killing vectors. This method consists in writing the axisymmetric stationry Einstein…
Using a new ansatz for solving the Einstein equations with a scalar field with the sign of the kinetic term inverted, I find a series of formulae to derive axial symmetric stationary exact solutions of the Phantom scalar field in general…
In the present paper we consider the Einstein-multiple-scalar field theory. When the target space of the scalar fields is a complete, simply connected Riemannian manifold with non-positive sectional curvature we prove that the static and…
We investigate oscillating instanton solutions of a self-gravitating scalar field between degenerate vacua. We show that there exist O(4)-symmetric oscillating solutions in a de Sitter background. The geometry of this solution is finite and…
Assuming conformally flat metric we obtain inhomogeneous solutions of Einstein equations with the energy-momentum of a viscous fluid. We suggest that the viscous solution can be applied as a model of an expanding inhomogeneous dark energy.
We extend the work in our earlier article [4] to show that time-periodic, asymptotically-flat solutions of the Einstein equations analytic at scri, whose source is one of a range of scalar-field models, are necessarily stationary. We also…
We investigate the Einstein equation with a positive cosmological constant for $4n+4$-dimensional metrics on bundles over Quaternionic K\"ahler base manifolds whose fibers are 4-dimensional Bianchi IX manifolds. The Einstein equations are…
A scheme is discussed for embedding n-dimensional, Riemannian manifolds in an (n+1)-dimensional Einstein space. Criteria for embedding a given manifold in a spacetime that represents a solution to Einstein's equations sourced by a massless…