Related papers: Trapped surfaces in spherical expanding open unive…
We generalize a theorem of Finkelstein and Moriah and show that if a link $L$ has a $2n$-plat projection satisfying certain conditions, then its complement contains some closed essential surfaces. In most cases these surfaces remain…
We derive integral and sup-estimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
Asymptotically flat, time-symmetric, axially symmetric and conformally flat initial data for vacuum general relativity are studied numerically on $R^3$ with the interior of a standard torus cut out. By the choice of boundary condition the…
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
We study the formation of marginally trapped surfaces in the head-on collision of two shock waves both in anti-de Sitter and Minkowski space-time in various dimensions as a function of the spread of the energy density in transverse space.…
A time-varying cosmological "constant" Lambda is consistent with Einstein's equation, provided matter and/or radiation is created or destroyed to compensate for it. Supposing an empty primordial universe endowed with a very large…
We derive the matching conditions for cosmological perturbations in a Friedmann Universe where the equation of state undergoes a sharp jump, for instance as a result of a phase transition. The physics of the transition which is needed to…
A general property of universes without initial singularity is investigated based on the singularity theorem, assuming the null convergence condition and the global hyperbolicity. As a direct consequence of the singularity theorem, the…
We present a generic condition for Lorentzian manifolds to have a barrier that limits the reach of boundary-anchored extremal surfaces of arbitrary dimension. We show that any surface with nonpositive extrinsic curvature is a barrier, in…
Recent observations indicate that the Universe is not transparent but partially opaque due to absorption of light by ambient cosmic dust. This implies that the Friedmann equations valid for the transparent universe must be modified for the…
In this article we study the shape of a compact surface of constant mean curvature of Euclidean space whose boundary is contained in a round sphere. We consider the case that the boundary is prescribed or that the surface meets the sphere…
We show that the causal set approach to creating an ever-present cosmological 'constant' in the expanding universe is strongly constrained by the isotropy of the microwave background. Fluctuations generated by stochastic lambda generation…
We present a new, fully anisotropic, criterion for formation of trapped surfaces in vacuum. More precisely we provide conditions on null data, concentrated in a neighborhood of a short null geodesic segment (possibly flat everywhere else)…
The main aim of this thesis is to study the properties of trapped surfaces in spacetimes with symmetries and their possible relation with the theory of black holes. We will concetrate specially on one aspect of this possible equivalence,…
Recent observations seem to indicate that we live in a universe whose spatial sections are nearly or exactly flat. Motivated by this we study the problem of observational detection of the topology of universes with flat spatial sections. We…
The necessary and sufficient condition for the absence of particle horizons in a big bang Friedmann-Robertson-Walker universe is provided. It happens to be a "smooth big bang" initial condition: the proper time derivative of the expansion…
Although big bang cosmology effectively models even the most puzzling observational data, it offers no insight into why the cosmological expansion should occur at all. In this paper it is suggested that a finite Universe poses particular…
The expansion of the closed two-component universe has been considered. The potential barrier of the expansion has been investigated and its overcoming condition has been obtained. The restrictions on the Friedmann integrals, cosmological…
In singularity generating spacetimes both the out-going and in-going expansions of null geodesic congruences $\theta ^{+}$ and $\theta ^{-}$ should become increasingly negative without bound, inside the horizon. This behavior leads to…