Related papers: The trapped region
One of the remarkable features of black holes is that they possess a thermodynamic description, even though they do not appear to be statistical systems. We use self-gravitating magnetic monopole solutions as tools for understanding the…
Black holes are presumed to have an ideal ability to absorb and keep matter. Whatever comes close to the event horizon, a boundary separating the inside region of a black hole from the outside world, inevitably goes in and remains inside…
A unifying definition of trapped submanifold for arbitrary codimension by means of its mean curvature vector is presented. Then, the interplay between (generalized) symmetries and trapped submanifolds is studied, proving in particular that…
Recently, new exploratory channels have opened up for the physics of highly compact objects, such as gravitational waves and black hole shadows. Moreover, more precise analysis and observations are now possible in the physics of accretion…
The work on black holes immersed in external fields is reviewed in both test-field approximation and within exact solutions. In particular we pay attention to the effect of the expulsion of the flux of external fields across charged and…
We consider an initial data set having a continuous symmetry and a marginally outer trapped surface (MOTS) that is not preserved by this symmetry. We show that such a MOTS is unstable except in an exceptional case. In non-rotating cases we…
We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.
We present a few general results on foliations of 4-manifolds by surfaces: existence, tautness, relations to minimal genus of embedded surfaces; as well as some open problems. We hope to stimulate interest in this area.
In [5], a rigidity result was obtained for outermost marginally outer trapped surfaces (MOTSs) that do not admit metrics of positive scalar curvature. This allowed one to treat the "borderline case" in the author's work with R. Schoen…
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…
In this article a new upper bounds for the multiple trigonometrical integrals are found. The method of the work based on a new method of estimation for the areas of algebraic surfaces.
Quadratic systems with lossless quadratic terms arise in many applications, including models of atmosphere and incompressible fluid flows. Such systems have a trapping region if all trajectories eventually converge to and stay within a…
In this chapter, we review some of the interesting consequences that tilt between the spin axis of the black hole and angular momentum axis of the accretion disk can have on the dynamics, thermodynamics, and observational appearance of…
Arguments for black hole formation in collisions of high-energy particles have rested on the emergence of a closed trapped surface in the classical geometry of two colliding Aichelburg-Sexl solutions. Recent analysis has, however, shown…
We present a notion of a random toric surface modeled on a notion of a random graph. We then study some threshold phenomena related to the smoothness of the resulting surfaces.
We give a brief introduction to some of the recent works on finding geometric structures on triangulated surfaces using variational principles.
This is a follow up on our previous work in which we have presented a modified, simpler version of the remarkable recent result of Christodoulou on the formation of trapped surfaces. In this paper we prove two related results. First we…
Some approaches to quantization of the horizon area of black holes are discussed. The maximum entropy of a quantized surface is demonstrated to be proportional to the surface area in the classical limit. This result is valid for a rather…
We continue the investigation of formation of trapped surfaces in strongly curved , conformally flat geometries. Initial data in quasi-polar gauges rather then maximal ones are considered. This implies that apparent horizons coincide with…
After a brief historical introduction, we summarize current efforts and accomplishments in the study of supermassive black holes.