Related papers: Trapped surfaces
When a lump of matter falls into a black hole it is expected that a marginally trapped tube when hit moves outwards everywhere, even in regions not yet in causal contact with the infalling matter. But to describe this phenomenon…
Surfaces with concentric $K$-contours and parallel $K$-contours in Euclidean $3$-space are defined. Crucial examples are presented and characterization of them are given.
We consider the formation of trapped surfaces in the evolution of the Einstein-scalar field system without symmetries. To this end, we follow An's strategy to analyse the formation of trapped surfaces in vacuum and for the Einstein-Maxwell…
We study the properties of the loosely trapped surface (LTS) and the dynamically transversely trapping surface (DTTS) in Einstein-Maxwell systems. These concepts of surfaces were proposed by the four of the present authors in order to…
I describe the general mathematical construction and physical picture of topological black holes, which are black holes whose event horizons are surfaces of non-trivial topology. The construction is carried out in an arbitrary number of…
We prove that finite area isolated singularities of surfaces with constant positive curvature in R^3 are removable singularities, branch points or immersed conical singularities. We describe the space of immersed conical singularities of…
For distant observers black holes are trapped spacetime domains bounded by apparent horizons. We review properties of the near-horizon geometry emphasizing the consequences of two common implicit assumptions of semiclassical physics. The…
Our understanding of space and time is probed to its depths by black holes. These objects, which appear as a natural consequence of general relativity, provide a powerful analytical tool able to examine macroscopic and microscopic…
Trapped regions bounded by horizons are the defining features of black holes. However, formation of a singularity-free apparent horizon in finite time of a distant observer is consistent only with special states of geometry and matter in…
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. In the present paper we find all marginally trapped surfaces with pointwise 1-type Gauss…
The lightlike geometry of codimension two spacelike submanifolds in Lorentz-Minkowski space has been developed in [Izumiya, S. and Romero Fuster, M. C. Selecta Mathematica (NS), 13 23--55 (2007)] which is a natural Lorentzian analogue of…
In this study we give definitions and characterizations of transversal surfaces of timelike ruled surfaces. We study some special cases such as the striction curve is a geodesic, an asymptotic line or a line of curvature. Moreover, we…
The question of whether an observer can escape from a black hole is addressed, using a recent general definition of a black hole in the form of a future outer trapping horizon. An observer on a future outer trapping horizon must enter the…
Seven different refinements of trapped surfaces are proposed, each intended as potential stability conditions. This article concerns spherical symmetry, but each condition can be generalized. Involute trapped spheres satisfy a similar…
It is a standard fact that trapped or marginally trapped surfaces are not visible from conformal infinity, under the usual set of conditions on matter fields and the conformal completion, provided that the cosmological constant is…
A general definition of a black hole is given, and general `laws of black-hole dynamics' derived. The definition involves something similar to an apparent horizon, a trapping horizon, defined as a hypersurface foliated by marginal surfaces…
Trapping by active sites on surfaces plays important roles in various chemical and biological processes, including catalysis, enzymatic reactions, and viral entry into host cells. However, the mechanisms of these processes remain not well…
Classes of branched surfaces extend the classes of surfaces or 2-dimensional manifolds satisfying suitable properties and defined in various manners. Reeb spaces of smooth maps of suitable classes into surfaces whose codimensions are…
Bounds for the area of general closed marginally trapped surfaces (MTSs) are presented. They do not require any stability condition, and are determined by a constant that depends on a particular component of the Einstein tensor on the…