Related papers: Cauchy problems for Einstein equations in three-di…
Multi-parameter solutions to the Einstein equations in 2+1 dimensions are presented, with stress-energy given by a rotating dust with negative cosmological constant. The matter density is uniform in the corotating frame, and the ratio of…
The intention of this article is to give a flavour of some global problems in General Relativity. We cover a variety of topics, some of them related to the fundamental concept of 'Cauchy hypersurfaces': (1) structure of globally hyperbolic…
We derive, in 3+1 spacetime dimensions, two alternative systems of quasi-linear wave equations, based on Friedrich's conformal field equations. We analyse their equivalence to Einstein's vacuum field equations when appropriate constraint…
The paper is concerned with sticky weak solutions to the equations of pressureless gases in two or more space dimensions. Various initial data are constructed, showing that the Cauchy problem can have (i) two distinct sticky solutions, or…
The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global…
We study the space-time geometry generated by coupling a free scalar field with a non-canonical kinetic term to General Relativity in $(2+1)$ dimensions. After identifying a family of scalar Lagrangians that yield exact analytical solutions…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
We study the Cauchy problem for a system of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the order…
We establish the existence of $1$-parameter families of $\epsilon$-dependent solutions to the Einstein-Euler equations with a positive cosmological constant $\Lambda >0$ and a linear equation of state $p=\epsilon^2 K \rho$, $0<K\leq 1/3$,…
An example of a solution branch of the three dimensional Euler equation Cauchy problem is constructed which develops a singular velocity component and a singular vorticity component after finite time for some data which have Hoelder…
The authors study the Cauchy problem of the magnetohydrodynamic equations for viscous compressible barotropic flows in two or three spatial dimensions with vacuum as far field density. For two spatial dimensions, we establish the global…
We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson--(anti)-de Sitter ((A)dS) metrics,…
Ricci-flat solutions to Einstein's equations in four dimensions are obtained as the flat limit of Einstein spacetimes with negative cosmological constant. In the limiting process, the anti-de Sitter energy--momentum tensor is expanded in…
A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a space-like and null hypersurface. The development of the data is obtained…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…
We formulate and analyze the Hamiltonian dynamics of a pair of massive spinless point particles in (2+1)-dimensional Einstein gravity by anchoring the system to a conical infinity, isometric to the infinity generated by a single massive but…
We consider the 3-dimensional formulation of Einstein's theory for spacetimes possessing a non-null Killing field $\xi^a$. It is known that for the vacuum case some of the basic field equations are deducible from the others. It will be…
We construct a large class of new singularity-free static Lorentzian four-dimensional solutions of the vacuum Einstein equations with a negative cosmological constant. The new families of metrics contain space-times with, or without, black…
In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In…
The Cauchy problem for the Maxwell-Klein-Gordon equations in Lorenz gauge in $n$ space dimensions ($n \ge 2$) is locally well-posed for low regularity data, in two and three space dimensions even for data without finite energy. The result…