相关论文: Physically Realistic Solutions to the Ernst Equati…
It is proved that the only geodesically complete stationary vacuum solution of the Einstein equations is the empty Minkowski space, or a quotient of it by a discrete group of isometries, generalizing a classical result of Lichnerowicz. In…
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 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…
This paper deals with the applications of weighted Besov spaces to elliptic equations on asymptotically flat Riemannian manifolds, and in particular to the solutions of Einstein's constraints equations. We establish existence theorems for…
This article explores solutions to a generalised form of the Seiberg--Witten equations in higher dimensions, first introduced by Fine and the author. Starting with an oriented $n$ dimensional Riemannian manifold with a…
The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is presented. The spacelike section of the class of metrics under consideration is a warped product of the real line with a nontrivial…
A class of stationary rigidly rotating perfect fluid coupled with non-linear electromagnetic fields was investigated. An exact solution of the Einstein equations with sources for the Carter B(+) branch was found, for the equation of state…
We show that an ansatz for $1+3+n$ dimensional static spacetime with spherical symmetry in three dimensions and Euclidean symmetry in $n$ dimensions, parametrized by only one function of radial coordinate, leads to a limited set of vacuum…
We present unique solutions of the Seiberg-Witten Monopole Equations in which the U(1) curvature is covariantly constant, the monopole Weyl spinor consists of a single constant component, and the 4-manifold is a product of two Riemann…
A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in…
We develop, via Arnold's geometric framework, a mechanism for constructing explicit, smooth, global-in-time, and typically non-stationary solutions of the incompressible Euler equations. The approach introduces a notion of generalized…
The FHP algorithm allows to obtain the relativistic multipole moments of a vacuum stationary axisymmetric solution in terms of coefficients which appear in the expansion of its Ernst's potential on the symmetry axis. First of all, we will…
Einstein field equations for anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities.…
In recent works we have constructed axisymmetric solutions to the Euler-Poisson equations which give mathematical models of slowly uniformly rotating gaseous stars. We try to extend this result to the study of solutions of the…
The collision of two plane gravitational waves in Einstein's theory of relativity can be described mathematically by a Goursat problem for the hyperbolic Ernst equation in a triangular domain. We use the integrable structure of the Ernst…
The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations…
The Harmonic Einstein equation is the vacuum Einstein equation supplemented by a gauge fixing term which we take to be that of DeTurck. For static black holes analytically continued to Riemannian manifolds without boundary at the horizon…
We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is…
Using the Euclidon method, a stationary solution of Einstein's vacuum equations was obtained, describing N rotating axially symmetric masses, which in the absence of rotation describes N arbitrary axially symmetric static masses, for…
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…