Related papers: A Reformulation of the Hoop Conjecture
We study the probability that a horizon appears when concentric shells of matter collide, by computing the horizon wave-function of the system. We mostly consider the collision of two ultra-relativistic shells, both shrinking and expanding,…
We investigate the validity of the hyperhoop conjecture, which claims to determine a necessary and sufficient condition for the formation of black hole horizons in higher-dimensional space-times. Here we consider momentarily static,…
We give a thorough description of the shape of rotating axisymmetric stable black-hole (apparent) horizons applicable in dynamical or stationary regimes. It is found that rotation manifests in the widening of their central regions…
The Hopf conjecture states that an even-dimensional, positively curved Riemannian manifold has positive Euler characteristic. We prove this conjecture under the additional assumption that a torus acts by isometries and has dimension bounded…
This article introduces the subject of quasi-local horizons at a level suitable for physics graduate students who have taken a first course on general relativity. It reviews properties of trapped surfaces and trapped regions in some simple…
The topology of the event horizon (TOEH) is usually believed to be a sphere. Nevertheless, some numerical simulations of gravitational collapse with a toroidal event horizon or the collision of event horizons are reported. Considering the…
A straightforward generalization of the celebrated uniqueness theorem to dimensions greater than four was recently found to fail in two pure gravity cases - the 5d rotating black ring and the black string on R^{3,1} * S^1. Two amendments…
A recent precise formulation of the hoop conjecture in four spacetime dimensions is that the Birkhoff invariant $\beta$ (the least maximal length of any sweepout or foliation by circles) of an apparent horizon of energy $E$ and area $A$…
It is logically possible that regularly evaporating black holes exist in nature. In fact, the prevalent theoretical view is that these are indeed the real objects behind the curtain in astrophysical scenarios. There are several proposals…
The object of this paper is the tameness conjecture which describes an arbitrary graded k-algebra homomorphism of polytopal rings. We give further evidence of this conjecture by showing supporting results concerning joins, multiples and…
We directly connect topological changes that can occur in mathematical three-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena. This work widens the bridge between topology…
To what extent are all astrophysical, dark, compact objects both black holes (BHs) and described by the Kerr geometry? We embark on the exercise of defying the universality of this remarkable idea, often called the "Kerr hypothesis". After…
This is a review of current black-hole theory, concentrating on local, dynamical aspects.
It was recently argued by Almheiri et al that black hole complementarity strains the basic rules of quantum information theory, such as monogamy of entanglement. Motivated by this argument, we develop a practical framework for describing…
We consider a system of black holes -- a simplest substitute of a system of point particles in the mechanics of general relativity -- and try to describe their motion with the help of entropic action: a sum of the areas of black hole…
In recent work on black hole entropy in non-perturbative quantum gravity, an action for the black hole sector of the phase space is introduced and (partially) quantized. We give a number of observations on this and related works. In…
Several general arguments indicate that the event horizon behaves as a stretched membrane. We propose using this relation to understand gravity and dynamics of black objects in higher dimensions. We provide evidence that (i) the…
Geometric inequalities of classical differential geometry are used to extend to higher dimensional spacetimes the Penrose-Gibbons isoperimetric inequalities and the hoop conjecture of general reltivity.
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 black hole information paradox is really a combination of two problems: the causality paradox and the entanglement problem. The causality paradox arises because in the semiclassical approximation infalling matter gets causally trapped…