Related papers: Weakly regular T2 symmetric spacetimes. The future…
We consider weakly regular Gowdy-symmetric spacetimes on T3 satisfying the Einstein-Euler equations of general relativity, and we solve the initial value problem when the initial data set has bounded variation, only, so that the…
We define the class of weakly regular spacetimes with T2 symmetry, and investigate their global geometry structure. We formulate the initial value problem for the Einstein vacuum equations with weak regularity, and establish the existence…
Gowdy's model of cosmological spacetimes is a much investigated subject in classical and quantum gravity. Depending on spatial topology recollapsing as well as expanding models are known. Several analytic tools were used in order to clarify…
Under weak regularity assumptions, only, we develop a fully geometric theory of vacuum Einstein spacetimes with T2 symmetry, establish the global well-posedness of the initial value problem for Einstein's field equations, and investigate…
We investigate the late-time asymptotics of future expanding, polarized vacuum Einstein spacetimes with T2-symmetry on T3, which, by definition, admit two spacelike Killing fields. Our main result is the existence of a stable asymptotic…
We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T3, and we construct matter spacetimes with low regularity. These spacetimes admit, both, impulsive…
This paper establishes novel bounds for Gowdy-symmetric Einstein-Euler spacetimes and completes the analysis, initiated by LeFloch and Rendall, of the global areal foliation for these spacetimes. We thus consider the initial value problem…
We consider a system of nonlinear wave equations with constraints that arises from the Einstein equations of general relativity and describes the geometry of the so-called Gowdy symmetric spacetimes on T3. We introduce two numerical…
Using the standard Whitney topologies on spaces of Lorentzian metrics, we show that the existence of causal incomplete geodesics is a $C^\infty$-generic feature within the class of spacetimes of a given dimension $n\geq 3$ that are stably…
We show a global existence theorem for Einstein-matter equations of $T^{3}$-Gowdy symmetric spacetimes with stringy matter. The areal time coordinate is used. It is shown that this spacetime has a crushing singularity into the past. From…
We extend Beem's three completeness notions -- finite compactness, timelike Cauchy completeness, and Condition A -- originally defined for spacetimes, to Lorentzian length spaces and study their relationships. We prove that finite…
This work discusses the apriori possible asymptotic behavior to the future, for (vacuum) space-times which are geodesically complete to the future and which admit a foliation by compact constant mean curvature Cauchy surfaces.
Recent work by the authors led to the development of a mathematical theory dealing with `second--order hyperbolic Fuchsian systems', as we call them. In the present paper, we adopt a physical standpoint and discuss the implications of this…
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 investigate suitable, physically motivated conditions on spacetimes containing certain submanifolds - the so-called {weakly trapped submanifolds} - that ensure, in a set of neighboring metrics with respect to a convenient topology, that…
The global extendibility of smooth causal geodesically incomplete spacetimes is investigated. Denote by $\gamma$ one of the incomplete non-extendible causal geodesics of a causal geodesically incomplete spacetime $(M,g_{ab})$. First, it is…
We show global existence theorems for Gowdy symmetric spacetimes with type IIB stringy matter. The areal and constant mean curvature time coordinates are used. Before coming to that, it is shown that a wave map describes the evolution of…
Gowdy spacetimes are generalized to admit two commuting spatial "local" Killing vectors, and some new varieties of them are presented, which are all closely related to Thurston's geometries. Explicit spatial compactifications, as well as…
Spherically symmetric spacetimes are ambient spaces for models of stellar collapse and inhomogeneous cosmology. We obtain results for the Weyl tensor and the covariant form of the Ricci tensor on general doubly warped (DW) spacetimes. In a…
Geodesics are studied in one of the Weyl metrics, referred to as the M--Q solution. First, arguments are provided, supporting our belief that this space--time is the more suitable (among the known solutions of the Weyl family) for…