Related papers: A density theorem for asymptotically hyperbolic in…

In [Discrete Contin. Dyn. Syst. \textbf{15} (2006), no. 3, 811--818.] Xia introduced a simple dynamical density basis for partially hyperbolic sets of volume preserving diffeomorphisms. We apply the density basis to the study of the…

We present a local gluing construction for general relativistic initial data sets. The method applies to generic initial data, in a sense which is made precise. In particular the trace of the extrinsic curvature is not assumed to be…

For non uniformly hyperbolic maps of the interval with exponential decay of correlations we prove that the law of closest return to a given point when suitably normalized is almost surely asymptotically exponential. A similar result holds…

In the first half of this article, we survey the new quasi-local and total angular momentum and center of mass defined in [9] and summarize the important properties of these definitions. To compute these conserved quantities involves…

We establish the positive energy theorem for weak asymptotically anti-de Sitter initial data sets with distributional curvature under the weak dominant energy condition.

In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and non-decreasing initial data. We remark that these…

In this paper we continue earlier investigations of evolutionary formulations of the Einstein vacuum constraint equations originally introduced by R\'{a}cz. Motivated by the strong evidence from these works that the resulting vacuum initial…

We define the (total) center of mass for suitably asymptotically hyperbolic time-slices of asymptotically anti-de Sitter spacetimes in general relativity. We do so in analogy to the picture that has been consolidated for the (total) center…

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…

In this paper, we continue our investigations of R\'acz's parabolic-hyperbolic formulation of the Einstein vacuum constraints. Our previous studies of the asymptotically flat setting provided strong evidence for unstable asymptotics which…

Andersson and Chru\'sciel showed that generic asymptotically hyperboloidal initial data sets admit polyhomogeneous expansions, and that only a non-generic subclass of solutions of the conformal constraint equations is free of logarithmic…

Given a collection of N solutions of the (3+1) vacuum Einstein constraint equations which are asymptotically Euclidean, we show how to construct a new solution of the constraints which is itself asymptotically Euclidean, and which contains…

A generalized positive energy theorem for spaces with asymptotic SUSY compactification involving non-symmetric data is proved. This work is motivated by the work of Dai [D1][D2], Hertog-Horowitz-Maeda [HHM], and Zhang [Z].

In this paper we consider the hyperbolic formulation of the constraints introduced by R\'acz. Using the numerical framework recently developed by us we construct initial data sets which can be interpreted as nonlinear perturbations of…

In Special Relativity, massless objects are characterized as either vacuum states or as radiation propagating at the speed of light. This distinction extends to General Relativity for asymptotically flat initial data sets (IDS) \((M^n, g,…

We prove the existence of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers…

We introduce a novel quantity for general dynamical systems, which we call the asymptotic uniform complexity. We prove an inequality relating the asymptotic uniform complexity of a dynamical system to its mean topological matching number.…

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…

We prove positive mass theorem with angular momentum and charges for axially symmetric, simply connected, maximal, complete initial data sets with two ends, one designated asymptotically flat and the other either (Kaluza-Klein)…

We show that asymptotically hyperbolic initial data satisfying smallness conditions in dimensions $n\ge 3$, or fast decay conditions in $n\ge 5$, or a genericity condition in $n\ge 9$, can be deformed, by a deformation which is supported…