相关论文: On the geometry and topology of initial data sets …

Based on scale critical initial data, we construct smooth asymptotically flat Cauchy initial data for the Einstein vacuum system that does not contain Marginally Outer Trapped Surfaces (MOTS) but whose future evolution contains a trapped…

Global properties of maximal future Cauchy developments of stationary, m-dimensional asymptotically flat initial data with an outer trapped boundary are analyzed. We prove that, whenever the matter model is well posed and satisfies the null…

This is the second and last paper of a two-part series in which we prove the $C^2$-formulation of the strong cosmic censorship conjecture for the Einstein-Maxwell-(real)-scalar-field system in spherical symmetry for two-ended asymptotically…

Motivated by recent interest in black holes whose asymptotic geometry approaches that of anti-de Sitter spacetime, we give a proof of topological censorship applicable to spacetimes with such asymptotic behavior. Employing a useful…

The aim of this work is to present an initial data version of Hawking's theorem on the topology of back hole spacetimes in the context of manifolds with boundary. More precisely, we generalize the results of G. J. Galloway and R. Schoen…

We introduce a natural generalization of marginally outer trapped surfaces, called immersed marginally outer trapped surfaces, and prove that three dimensional asymptotically flat initial data sets either contain such surfaces or are…

In [5], a rigidity result was obtained for outermost marginally outer trapped surfaces (MOTSs) that do not admit metrics of positive scalar curvature. This allowed one to treat the "borderline case" in the author's work with R. Schoen…

We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations…

We investigate existence and uniqueness of solutions of the Cauchy problem for the porous medium equation on a class of Cartan-Hadamard manifolds. We suppose that the radial Ricci curvature, which is everywhere nonpositive as well as…

We consider the wave equation on Reissner-Nordstr\"om-de Sitter and more generally Kerr-Newman-de Sitter black hole spacetimes with $\Lambda>0$. The strength of the blue-shift instability associated to the Cauchy horizon of these spacetimes…

This is the first and main paper of a two-part series, in which we prove the $C^{2}$-formulation of the strong cosmic censorship conjecture for the Einstein-Maxwell-(real)-scalar-field system in spherical symmetry for two-ended…

It has been argued that the strong cosmic censorship conjecture is violated by Reissner-Nordstr\"om-de Sitter black holes: for near-extremal black holes, generic scalar field perturbations arising from smooth initial data have finite energy…

The theory of General Relativity predicts that black holes are a natural constituent of our Universe. Before a black hole binary relaxes to a final state, it undergoes damped oscillations which completely characterize the final object.…

An outstanding issue in the treatment of boundaries in general relativity is the lack of a local geometric interpretation of the necessary boundary data. For the Cauchy problem, the initial data is supplied by the 3-metric and extrinsic…

We examine the $C^{0}$-formulation of the strong cosmic censorship conjecture (SCC) from a quantum complexity-theoretic perspective and argue that for generic black hole parameters as initial conditions for the Einstein equations,…

In gr-qc/9902061 it was shown that (n+1)-dimensional asymptotically anti-de-Sitter spacetimes obeying natural causality conditions exhibit topological censorship. We use this fact in this paper to derive in arbitrary dimension relations…

We study Cauchy initial data for asymptotically flat, stationary vacuum space-times near space-like infinity. The fall-off behavior of the intrinsic metric and the extrinsic curvature is characterized. We prove that they have an analytic…

In classical General Relativity, the values of fields on spacetime are uniquely determined by their values at an initial time within the domain of dependence of this initial data surface. However, it may occur that the spacetime under…

In this article we investigate the restrictions imposed by the dominant energy condition (DEC) on the topology and conformal type of \textsl{possibly non-compact} marginally outer-trapped surfaces (thus extending Hawking's classical theorem…

Conformal mappings of surfaces of constant mean curvature onto compact bounded background spaces are constructed for Minkowski space-time and for Schwarzschild black hole spacetimes. In the black hole example, it is found that initial data…