Related papers: A Reformulation of the Hoop Conjecture
We study the condition of black hole formation in five-dimensional space-time. We analytically solve the constraint equations of five-dimensional Einstein equations for momentarily static and conformally flat initial data of a spheroidal…
We determine the causal structure of the McVittie spacetime for a cosmological model with an asymmetric bounce. The analysis includes the computation of trapping horizons, regular, trapped, and anti-trapped regions, and the integration of…
The topological structure of the event horizon has been investigated in terms of the Morse theory. The elementary process of topological evolution can be understood as a handle attachment. It has been found that there are certain…
In this paper we define the bi-orthogonal sectional curvature and we present two modified Yamabe invariants for compact 4-dimensional manifolds. In particular we obtained a relationship between one of these invariants and a Hopf conjecture.
In analyzing maximally symmetric Lovelock black holes with non-planar horizon topologies, many novel features have been observed. The existence of finite radius singularities, a mass gap in the black hole spectrum and solutions displaying…
A novel approach to understanding the hierarchy problem is presented making use of topological aspects of the renormalisation group and the ER-EPR interpretation of entanglement. A common discussion of the renormalisation group, the black…
Introducing the concept of the extreme trapping horizon, we discuss geometric features of dynamical extreme black holes in four dimensions and then derive the integral identities which hold for the dynamical extreme black holes. We address…
This work is originally a Cambridge Part III essay. Throughout the paper, some aspects of General Relativity in higher dimensions are reviewed. The work presented draws a path within the wide landscape of higher dimensional black holes…
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…
The trapping (or apparent) horizon serves as a key tool for tracing the complete evolution of black holes. We investigate a class of coordinate singularities induced by such trapping (or apparent) horizons in a spherically symmetric,…
Recently, with numerical methods, Hod clarified the validity of Thorne hoop conjecture for spatially regular static charged fluid spheres, which were considered as counterexamples against the hoop conjecture. In this work, we provide an…
In gravitational collapse leading to black hole formation, trapping horizons typically develop inside the contracting matter. Classically, an ingoing trapping horizon moves towards the centre where it reaches a curvature singularity, while…
We investigate a stronger formulation of Webb's conjecture on the contractibilty of the orbit space of the p-subgroup complexes in terms of finite topological spaces. The original conjecture, which was first proved by Symonds and, more…
Black holes are capable of reflection: there is a finite probability for any particle that approaches the event horizon to bounce back. The albedo of the black hole depends on its temperature and the energy of the incoming particle. The…
After a brief reminscence about work with K. Sato 25 years ago on the monopole problem and inflation, a discussion is given of the black hole information paradox. It is argued that, quite generally, it should be anticipated that the states…
Closely packed conformations of helices formed on the ideal rope are considered. The pitch versus radius relations which define a closely packed helix are determined. The relations stem from the turn-to-turn distance and curvature limiting…
We discuss the relation between the concentration of the Brown-York mass and the formation of trapped surfaces in non-spherical massive systems. In particular, we formulate and prove a precise version of the Thorne hoop conjecture in…
Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…
The process of black hole evaporation resulting from the Hawking effect has generated an intense controversy regarding its potential conflict with quantum mechanics' unitary evolution. In a recent couple of works of a collaboration…
Since the Weak Cosmic Censorship Conjecture was proposed, research on this conjecture has been ongoing. This paper explores the conjecture in black holes that are closer to those existing in the real universe (i.e., rotating black holes…