Related papers: Trapped surfaces
The indicatrix or curvature ellipse and the characteristic curve of a surface in $\mathbf R^4$ are presented, as well as the projective duality connecting them. The characterisation of points in the surfaces as elliptic, parabolic and…
We formulate problems of tight closure theory in terms of projective bundles and subbundles. This provides a geometric interpretation of such problems and allows us to apply intersection theory to them. This yields new results concerning…
We consider a simple, physical approach to the problem of marginally trapped surfaces in the Nonsymmetric Gravitational Theory (NGT). We apply this approach to a particular spherically symmetric, Wyman sector gravitational field, consisting…
A marginally outer trapped hypersurface is a generalization of minimal hypersurfaces originated from general relativity. We show a curvature estimate for stable marginally outer trapped hypersurfaces up to the free boundary satisfying a…
Recent calculations have shown that the linear proportionality between black hole entropy and area can be explained by performing a density matrix calculation for a massless free field theory. By applying the same formalism to an empirical…
In this talk, I present and discuss a number of attempts to construct black hole solutions in models with Warped Extra Dimensions. Then, a contact is made with models with Large Extra Dimensions, where black-hole solutions are easily…
This chapter briefly discusses the fundamental properties of black holes in general relativity, the discovery of astrophysical black holes and their main astronomical observations, how X-ray and $\gamma$-ray facilities can study these…
When studying the causal propagation of a field in a globally hyperbolic spacetime M, one often wants to express the physical intuition that it has compact support in spacelike directions, or that its support is a spacelike compact set. We…
Optimizing an implicational base of a closure system consists in turning this implicational base into an equivalent one with premises and conclusions as small as possible. This task is known to be hard in general but tractable for a number…
We consider closed and orientable immersed hypersurfaces of translational manifolds. Given a vector field on such a hypersurface, we define a perturbation of its Gauss map, which allows us to obtain topological invariants for the immersion…
In this paper, based on the theory of surfaces in the four-dimensional Euclidean space which generalizes the theory of surfaces in three-dimensional Euclidean space, beside other results, we will give a characterization of points on…
Working in infinite dimensional linear spaces, we deal with support for closed sets without interior. We generalize the Convexity Theorem for closed sets without interior. Finally we study the infinite dimensional version of Jordan…
We use convergence theory as the framework for studying H-closed spaces and H-sets in topological spaces. From this viewpoint, it becomes clear that the property of being H-closed and the property of being an H-set in a topological space…
A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be…
We recall fundamental aspects of the pluriclosed flow equation and survey various existence and convergence results, and the various analytic techniques used to establish them. Building on this, we formulate a precise conjectural…
Consider a domain D in R^3 which is convex (possibly all R^3) or which is smooth and bounded. Given any open surface M, we prove that there exists a complete, proper minimal immersion f : M --> D. Moreover, if D is smooth and bounded, then…
We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note.
We classify the singular loci of real surfaces in three-space that contain two circles through each point. We characterize how a circle in such a surface meets this loci as it moves in its pencil and as such provide insight into the…
In this note, we survey recent advances in the study of dynamical properties of the space of surfaces with constant curvature in three-dimensional manifolds of negative sectional curvature. We interpret this space as a two-dimensional…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…