Related papers: Construction of Initial Data Associated to the Cha…
We revisit Winicour's affine-null metric initial value formulation of General Relativity, where the characteristic initial value formulation is set up with a null metric having two affine parameters. In comparison to past work, where the…
In this work a new numerical technique to prepare Cauchy data for the initial value problem (IVP) formulation of Einstein's field equations is presented. Directly inspired by the exterior asymptotic gluing (EAG) result of Corvino (2000) our…
We show how to prescribe the initial data of a characteristic problem satisfying the costraints, the smallness, the regularity and the asymptotic decay suitable to prove a global existence result. In this paper, the first of two, we show 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…
Spacetime is foliated by spatial hypersurfaces in the 3+1 split of General Relativity. The initial value problem then consists of specifying initial data for all relevant fields on one such a spatial hypersurface. These fields are the…
In this paper we develop a new approach to the gluing problem in General Relativity, that is, the problem of matching two solutions of the Einstein equations along a spacelike or characteristic (null) hypersurface. In contrast to the…
Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through…
We investigate the existence and the global causal structure of plane symmetric spacetimes with weak regularity when the matter consists of an irrotational perfect fluid with pressure equal to its mass-energy density. Our theory encompasses…
We revisit and generalize, to the Einstein-Yang-Mills-Higgs system, previous results of D. Christodoulou and D. Chae concerning global solutions for the Einstein-scalar field and the Einstein-Maxwell-Higgs equations. The novelty of the…
The regular finite initial value problem at infinity is used to obtain regularity conditions on the freely specifiable parts of initial data for the vacuum Einstein equations with non-vanishing second fundamental form. These conditions…
The Einstein-Yang-Mills equations are the source of many interesting solutions within general relativity, including families of particle-like and black hole solutions, and critical phenomena of more than one type. These solutions,…
We obtain necessary and sufficient conditions for an initial data set for the vacuum conformal Einstein field equations to give rise to a spacetime development in possession of a Killing spinor. The fact that the conformal Einstein field…
In this paper we study the spherically symmetric characteristic initial data problem for the Einstein-Maxwell-scalar field system with a positive cosmological constant in the interior of a black hole, assuming an exponential Price law along…
We describe conformally flat initial data, with explicitly given analytic extrinsic curvature solving the vacuum momentum constraints. They follow from a solution of Dain and Friedrich discovered in 2001. The cylindrically symmetric subcase…
We give ansatze for solving classically the initial value constraints of general relativity minimally coupled to a scalar field, electromagnetism or Yang-Mills theory. The results include both time-symmetric and asymmetric data. The…
We consider the Einstein-Maxwell-fluid constraint equations, and make use of the conformal method to construct and parametrize constant-mean-curvature hyperboloidal initial data sets that satisfy the shear-free condition. This condition is…
We present a new initial data formulation to solve the full set of Einstein equations for spacetimes that contain a black hole under general conditions. The method can be used to construct complete initial data for spacetimes (the full…
We solve the Einstein constraint equations for a first-order causal viscous relativistic hydrodynamic theory in the case of a conformal fluid. For such a theory, a direct application of the conformal method does not lead to a decoupling of…
It is well-known that small, regular, spherically symmetric characteristic initial data to the Einstein-scalar-field system which are decaying towards (future null) infinity give rise to solutions which are foward-in-time global (in the…
Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…