Related papers: Solutions of special asymptotics to the Einstein c…
In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…
In this note we examine some recently proposed solutions of the linearized vacuum Einstein equations. We show that such solutions are {\it not} symmetries of the Einstein equations, because of a crucial integrability condition.
A general framework for the solutions of the constraints of pure gravity is constructed. It provides with well defined mathematical criteria to classify their solutions in four classes. Complete families of solutions are obtained in some…
The classification of solutions of the static vacuum Einstein equations, on a given closed manifold or an asymptotically flat one, is a long-standing and much-studied problem. Solutions are characterized by a complete Riemannian…
In this paper, we introduce new methods for solving the vacuum Einstein constraints equations: the first one is based on Schaefer's fixed point theorem (known methods use Schauder's fixed point theorem) while the second one uses the concept…
The Einstein constraint equations have been the subject of study for more than fifty years. The introduction of the conformal method in the 1970's as a parameterization of initial data for the Einstein equations led to increased interest in…
We show that all solutions to the vacuum Einstein field equations may be mapped to instanton configurations of the Ashtekar variables. These solutions are characterized by properties of the moduli space of the instantons. We exhibit…
We give a definition and derive the equations of motion for the center of mass and angular momentum of an axially symmetric, isolated system that emits gravitational and electromagnetic radiation. A central feature of this formulation is…
We discuss the existence of solutions with oblique asymptotes to a class of second order nonlinear ordinary differential equations by means of Lyapunov functions. The approach is new in this field and allows for simpler proofs of general…
We consider the Einstein equation with first order (semiclassical) quantum corrections. Although the quantum corrections contain up to fourth order derivatives of the metric, the solutions which are physically relevant satisfy a reduced…
The main purpose of this monograph is to give an elementary and self-contained account of the existence of asymptotically hyperbolic Einstein metrics with prescribed conformal infinities sufficiently close to that of a given asymptotically…
In this paper, we continue our investigations of R\'acz's parabolic-hyperbolic formulation of the Einstein vacuum constraints. Our previous studies of the asymptotically flat setting provided strong evidence for unstable asymptotics which…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
In this article we further develop the solution theory for the Einstein constraint equations on an n-dimensional, asymptotically Euclidean manifold M with interior boundary S. Building on recent results for both the asymptotically Euclidean…
New axisymmetric stationary solutions of the vacuum Einstein equations in five-dimensional asymptotically flat spacetimes are obtained by using solitonic solution-generating techniques. The new solutions are shown to be equivalent to the…
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
We construct new examples of complete Einstein metrics on balls. At each point of the boundary at infinity, the metric is asymptotic to a homogeneous Einstein metric on a solvable group, which varies with the point at infinity.
Asymptotic formula is derived for the behavior of the fundamental solution of the second-order elliptic self-adjoint operator with a piecewise-smooth coefficient in front of the senior derivatives near the discontinuity surface of the…
We construct new solutions of the vacuum Einstein field equations with multiple NUT parameters, with and without cosmological constant. These solutions describe spacetimes with non-trivial topology that are asymptotically dS, AdS or flat.…