Related papers: Trapped surfaces and spherical closed cosmologies

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 study the location of marginally trapped surfaces in space-times resulting from an axial deformation of static isotropic systems, and show that the Misner-Sharp mass evaluated on the corresponding undeformed spherically symmetric space…

Random packings of objects of a particular shape are ubiquitous in science and engineering. However, such jammed matter states have eluded any systematic theoretical treatment due to the strong positional and orientational correlations…

We prove a topological rigidity theorem for closed hypersurfaces of the Euclidean sphere and of an elliptic space form. It asserts that, under a lower bound hypothesis on the absolute value of the principal curvatures, the hypersurface is…

Given a spacelike foliation of a spacetime and a marginally outer trapped surface S on some initial leaf, we prove that under a suitable stability condition S is contained in a ``horizon'', i.e. a smooth 3-surface foliated by marginally…

The holographic prescription for computing entanglement entropy requires that the bulk extremal surface, whose area encodes the amount of entanglement, satisfies a homology constraint. Usually this is stated as the requirement of a…

Recently a simple proof of the generalizations of Hawking's black hole topology theorem and its application to topological black holes for higher dimensional ($n\geq 4$) spacetimes was given \cite{rnew}. By applying the associated new line…

We consider flat Friedmann-Lema\^{\i}tre-Robertson-Walker cosmological models in the framework of general scalar-tensor theories of gravity with arbitrary coupling functions, set in the Jordan frame, in the cosmological epoch when the…

We consider Friedmann-Lema\^{\i}tre-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological…

Extension of particle symmetry implies new conserved charges and the lightest particles, possessing such charges, should be stable. Created in early Universe, stable charged heavy leptons and quarks can exist and, hidden in elusive atoms…

We show that if a closed $C^1$-smooth surface in a Riemannian manifold has bounded Kolasinski--Menger energy, then it can be triangulated with triangles whose number is bounded by the energy and the area. Each of the triangles is an image…

Assuming that the dominant contribution, to the entropy due to entanglement across a spherical hypersurface, comes from the near horizon degrees of freedom, we analytically derive the entropy of a free massless scalar field in Minkowski…

We introduce a natural generalization of marginally outer trapped surfaces, called immersed marginally outer trapped surfaces, and prove that three dimensional asymptotically flat initial data sets either contain such surfaces or are…

Let X be a closed surface of genus two embedded in the 3-sphere. Then X inherits a metric and an orientation, which give an almost complex structure, which automatically integrates to a genuine complex structure, making X a Riemann surface.…

General relativity does not allow one to specify the topology of space, leaving the possibility that space is multi-- rather than simply--connected. We review the main mathematical properties of multi--connected spaces, and the different…

We prove that the boundary of the trapped region in an asymptotically Euclidean Riemannian manifold of dimension at least 3 is a stable smooth minimal hypersurface except for a singular set of codimension at least 8.

We investigate the geometric properties of marginally trapped surfaces (surfaces which have null mean curvature vector) in the spaces of oriented geodesics of Euclidean 3-space and hyperbolic 3-space, endowed with their canonical neutral…

The space-like hypersurface of the Universe at the present cosmological time is a three-dimensional manifold. A non-trivial global topology of this space-like hypersurface would imply that the apparently observable universe (the sphere of…

[Abridged] In a Universe with a detectable nontrivial spatial topology the last scattering surface contains pairs of matching circles with the same distribution of temperature fluctuations - the so-called circles-in-the-sky. Searches for…

Consider a spherically symmetric spacelike slice through a spherically symmetric spacetime. One can derive a universal bound for the optical scalars on any such slice. The only requirement is that the matter sources satisfy the dominant…