Related papers: On the breakdown criterion in General Relativity
Based on the canonical quantization of $d>2$ dimensional general relativity (GR) via the Dirac constraint formalism (also termed as `constraint quantization'), we propose the loss of covariance as a fundamental property of the theory. This…
This is the main paper in a sequence in which we give a complete proof of the bounded $L^2$ curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the…
We hereby show that the Kasner spacetime turns out to be singularity-free in Einstein's conformal gravity in vacuum or in presence of matter. Such a statement is based on the regularity of the curvature invariants and on the geodesic…
In order to specify a foliation of spacetime by spacelike hypersurfaces we need to place some restriction on the initial data and from this derive a way to calculate the lapse function $\alpha$ which measures the proper time and interval…
In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. We call such a manifold rigid if the universal cover of the base is Einstein or is isometric to a product of Einstein manifolds. When the…
We consider the 3-dimensional formulation of Einstein's theory for spacetimes possessing a non-null Killing field $\xi^a$. It is known that for the vacuum case some of the basic field equations are deducible from the others. It will be…
We study the geometry of a codimension-one foliation with a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as the Riemannian metric varies along the leaves of the foliation.…
We give necessary and sufficient conditions for warped product manifolds with 1-dimensional base, and in particular, for generalized Robertson-Walker spacetimes, to satisfy some generalized Einstein metric condition. We also construct…
The general class of Robinson-Trautman metrics that describe gravitational radiation in the exterior of bounded sources in four space-time dimensions is shown to admit zero curvature formulation in terms of appropriately chosen…
In this paper we prove a global existence theorem, in the direction of cosmological expansion, for sufficiently small perturbations of a family of $n+1$-dimensional, $n \geq 3$, spatially compact spacetimes which generalizes the $k=-1$…
The notion of maximal extension of a globally hyperbolic space-time arises from the notion of maximal solutions of the Cauchy problem associated to the Einstein's equations of general relativity. In 1969 Choquet-Bruhat and Geroch proved…
We consider Einstein's equations coupled to the Euler equations in plane symmetry, with compact spatial slices and constant mean curvature time. We show that for a wide variety of equations of state and a large class of initial data,…
In the time-space symmetric version of dynamical triangulation, a non-perturbative version of quantum Einstein gravity, numerical simulations without matter have shown two phases, with spacetimes that are either crumpled or elongated like…
Motivated by situations with temporal evolution and spatial symmetries both singled out, we develop a new 2+1+1 decomposition of spacetime, based on a nonorthogonal double foliation. Time evolution proceeds along the leaves of the spatial…
A theorem about local in time existence of spacelike foliations with prescribed mean curvature in cosmological spacetimes will be proved. The time function of the foliation is geometrically defined and fixes the diffeomorphism invariance…
As it is well known, the global structure of the Einstein equations for general relativity in the context of the initial value problem, is a difficult and intricate mathematical problem. Therefore, any additional structure in their…
By using geometric methods and superenergy tensors, we find new simple criteria for the causal propagation of physical fields in spacetimes of any dimension. The method can be applied easily to many different theories and to arbitrary…
The large scale structure formation in the standard Einstein gravity at later time is uniquely determined by the expansion history H(z) measured by the geometrical factor. A possible departure from the expected standard structure formation…
In this work, we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We investigate conditions for the leaves being stable, totally geodesic or totally umbilical. We consider that…
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…