Related papers: Developments of initial data on big bang singulari…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
We study the plane-symmetric collision of two gravitational waves and describe the global spacetime geometry generated by this collision. To this end, we formulate the characteristic initial value problem for the Einstein equations, when…
Results on the behaviour in the past time direction of cosmological models with collisionless matter and a cosmological constant $\Lambda$ are presented. It is shown that under the assumption of non-positive $\Lambda$ and spherical or plane…
The spherically symmetric Einstein-Vlasov system is considered in Schwarzschild coordinates and in maximal-isotropic coordinates. An open problem is the issue of global existence for initial data without size restrictions. The main purpose…
The problem of constructing naked singularities in general relativity can be naturally divided into two parts: (i) the construction of the region exterior to the past light cone of the singularity, extending all the way to (an incomplete)…
The celebrated geodesic congruence equation of Raychaudhuri, together with the resulting singularity theorems of Penrose and Hawking that it enabled, yield a highly general set of conditions under which a spacetime (or, more generically, a…
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…
We discuss here the issue of regularity of initial data for dynamical spherically symmetric massless scalar field models in a spacetime. Generalizing the known solutions of Einstein equations given in this case by Wyman and Roberts, we…
We show the existence of complete, asymptotically flat Cauchy initial data for the vacuum Einstein field equations, free of trapped surfaces, whose future development must admit a trapped surface. Moreover, the datum is exactly a constant…
A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a space-like and null hypersurface. The development of the data is obtained…
In this article we show that one can construct initial data for the Einstein equations which satisfy the vacuum constraints. This initial data is defined on a manifold with topology $R^3$ with a regular center and is asymptotically flat.…
The conformal structure of the Schwarzschild-de Sitter spacetime is analysed using the extended conformal Einstein field equations. To this end, initial data for an asymptotic initial value problem for the Schwarzschild-de Sitter spacetime…
In this paper, we study the problem of the nonlinear interaction of impulsive gravitational waves for the Einstein vacuum equations. The problem is studied in the context of a characteristic initial value problem with data given on two null…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
We generalize Ringstr\"om's global future causal stability results (Ringstr\"om 2009) for certain expanding cosmological solutions of the Einstein-scalar field equations to solutions of the Einstein-Maxwell-scalar field system. In…
We present a new scheme for constructing initial data for the Einstein field equations using the conformal thin-sandwich formulation that does not assume conformal flatness or approximate Killing vectors. This includes a method for…
We prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with Schwartzschild solution in the neighborhood of space-like infinity. The result…
We develop the mathematics needed to treat the interaction of geometry and stress at any isotropic spacetime singularity. This enables us to handle the Einstein equations at the initial singularity and characterize allowed general…
We construct a class of time-symmetric initial data sets for the Einstein vacuum equation modeling elementary configurations of multiple ``almost isolated" systems. Each such initial data set consists of a collection of several localized…
We are concerned with the formation of singularities and the existence of global continuous solutions of the Cauchy problem for the one-dimensional non-isentropic Euler equations for compressible fluids. For the isentropic Euler equations,…