Related papers: Revisiting the characteristic initial value proble…
Pursuing our analysis of [1], we study the gravitational solution space around a null hypersurface in the bulk of spacetime, such as a black hole or a cosmological horizon. We discuss the corresponding characteristic initial value problem…
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…
We prove the well-posedness of the initial boundary value problem for the Einstein equations with sole boundary condition the requirement that the timelike boundary is totally geodesic. This provides the first well-posedness result for this…
In the first of two papers, we study the initial boundary-value problem that underlies the theory of the Boltzmann equation for general non-spherical hard particles. In this work, for two congruent ellipses and for a large class of…
We discuss the initial value problem for the Einstein equations in Hitchin's generalised geometry for the case of closed divergence (which correspond to the equations of motion in the bosonic part of the NS-NS sector in type II…
This talk describes some recent results [16] regarding the problem of uniqueness in the large (also known as strong cosmic censorship) for the initial value problem in general relativity. In order to isolate the essential analytic features…
This is the second paper in a series of papers adressing the characteristic gluing problem for the Einstein vacuum equations. We solve the codimension-$10$ characteristic gluing problem for characteristic data which are close to the…
We consider the initial boundary value problem for the Einstein vacuum equations in the maximal gauge, or more generally, in a gauge where the mean curvature of a timelike foliation is fixed near the boundary. We prove the existence of…
We study the exterior solution for a static, spherically symmetric source in Weyl conformal gravity in terms of the Newman--Penrose formalism. We first show that both the static, uncharged black hole solution of Mannheim and Kazanas and the…
We construct the spacetime in the vicinity of a general isolated, rotating, charged black hole. The black hole is modeled as a weakly isolated horizon, and we use the characteristic initial value formulation of the Einstein equations with…
In this paper we study a numerical implementation for the initial boundary value formulation for the generalized conformal field equations. We propose a formulation which is well suited for the study of the long-time behaviour of perturbed…
In this article we show that one can construct initial data for the Einstein equations which satisfy the vacuum constraints. This initial data is defined on a manifold with topology $R^3$ with a regular center and is asymptotically flat.…
The characteristic initial (boundary) value problem has numerous applications in general relativity (GR) involving numerical studies, and is often formulated using Bondi-like coordinates. Recently it was shown that several prototype…
This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students…
We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…
This thesis is framed within the field of Mathematical Relativity and is organized into six chapters. After an introduction to the topic in Chapter 1, Chapter 2 reviews and further develops the formalism of hypersurface data, which provides…
This paper resolves the characteristic initial data problem for the three-dimensional compressible Euler equations - an open problem analogous to Christodoulou's characteristic initial value formulation for the vacuum Einstein field…
The main goal of this work consists in showing that the analytic solutions for a class of characteristic problems for the Einstein vacuum equations have an existence region larger than the one provided by the Cauchy-Kowalevski theorem, due…
The form of the initial value constraints in Ashtekar's hamiltonian formulation of general relativity is recalled, and the problem of solving them is compared with that in the traditional metric variables. It is shown how the general…
This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…