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In this note, we give a geometric characterization of the compact and totally umbilical hypersurfaces that carry a non trivial locally static Killing Initial Data (KID). More precisely, such compact hypersurfaces have constant mean…
We analyze Killing Initial Data on Cauchy surfaces in conformally rescaled vacuum space-times satisfying Friedrich's conformal field equations. As an application, we derive the KID equations on a spacelike $\mathcal{J}^-$.
We find necessary and sufficient conditions ensuring that the vacuum development of an initial data set of the Einstein's field equations admits a conformal Killing vector. We refer to these conditions as conformal Killing initial data…
The global characteristic initial value problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown…
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…
The initial value problem is well-defined on a class of spacetimes broader than the globally hyperbolic geometries for which existence and uniqueness theorems are traditionally proved. Simple examples are the time-nonorientable spacetimes…
In this paper we study the spacelike-characteristic Cauchy problem for the Einstein vacuum equations. We prove that given initial data on a maximal compact spacelike hypersurface $\Sigma \simeq \overline{B(0,1)} \subset \mathbb{R}^3$ and…
We analyze vacuum Killing Initial Data on characteristic Cauchy surfaces. A general theorem on existence of Killing vectors in the domain of dependence is proved, and some special cases are analyzed in detail, including the case of…
The existence of symmetries in asymptotically flat space-times are studied from the point of view of initial value problems. General necessary and sufficient (implicit) conditions are given for the existence of Killing vector fields in the…
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…
Conformal Killing equations and their integrability conditions for expanding hyperheavenly spaces with Lambda in spinorial formalism are studied. It is shown that any conformal Killing vector reduces to homothetic or isometric Killing…
In this paper, we consider the initial value problem for the Einstein-Vlasov-Scalar field equations in temporal gauge, where the initial data are prescribed on two characteristic smooth intersecting hypersurfaces. From a suitable choice of…
We construct compact initial data of constant mean curvature $\widetilde{K}$ for Einstein's 4d vacuum equations with $\widehat{\Lambda} = \Lambda - (\widetilde{K}^2/3)$ positive, where $\Lambda$ is the cosmological constant, via the…
Given an initial-boundary value problem for an anti-de Sitter-like spacetime, we analyse conditions on the conformal boundary ensuring the existence of Killing vectors in the spacetime arising from this problem. This analysis makes use of a…
As complement to Class. Quantum Grav. 30 (2013) 235036 we analyze Killing initial data on characteristic Cauchy surfaces in conformally rescaled vacuum spacetimes satisfying Friedrich's conformal field equations. As an application, we…
In a spacetime $(\mathcal{M},g)$, a horizon is a null hypersurface where the deformation tensor $\mathcal{K}:=\pounds_{\eta}g$ of a null and tangent vector $\eta$ satisfies certain restrictions. In this work, we develop a formalism to study…
We prove that any smooth vacuum spacetime containing a compact Cauchy horizon with surface gravity that can be normalised to a non-zero constant admits a Killing vector field. This proves a conjecture by Moncrief and Isenberg from 1983…
We study space-time Killing vectors in terms of their "lapse and shift" relative to some spacelike slice. We give a necessary and sufficient condition in order for these lapse-shift pairs, which we call Killing initial data (KID'S), to form…
We prove that generic solutions of the vacuum constraint Einstein equations do not possess any global or local space-time Killing vectors, on an asymptotically flat Cauchy surface, or on a compact Cauchy surface with mean curvature close to…
A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely…