Topology of Event Horizons and Topological Censorship

We prove that, under certain conditions, the topology of the event horizon of a four dimensional asymptotically flat black hole spacetime must be a 2-sphere. No stationarity assumption is made. However, in order for the theorem to apply, the horizon topology must be unchanging for long enough to admit a certain kind of cross section. We expect this condition is generically satisfied if the topology is unchanging for much longer than the light-crossing time of the black hole. More precisely, let $M$ be a four dimensional asymptotically flat spacetime satisfying the averaged null energy condition, and suppose that the domain of outer communication \C_K to the future of a cut $K$ of \Sm is globally hyperbolic. Suppose further that a Cauchy surface $\Sigma$ for \C_K is a topological 3-manifold with compact boundary $\partial\S$ in $M$, and $\S'$ is a compact submanifold of \bS with spherical boundary in $\S$ (and possibly other boundary components in $M/\S$). Then we prove that the homology group $H_1(\Sigma',Z)$ must be finite. This implies that either $\partial\S'$ consists of a disjoint union of 2-spheres, or $\S'$ is nonorientable and $\partial\S'$ contains a projective plane. Further, \partial\S=\partial\Ip[K]\cap\partial\Im[\Sp], and $\partial \Sigma$ will be a cross section of the horizon as long as no generator of \partial\Ip[K] becomes a generator of \partial\Im[\Sp]. In this case, if $\S$ is orientable, the horizon cross section must consist of a disjoint union of 2-spheres.}Comment: 11 pages, plain latex (minor revision: $\Sigma$ replaced by its closure in various places.

Stable Topologies of Event Horizon

In our previous work, it was shown that the topology of an event horizon (EH) is determined by the past endpoints of the EH. A torus EH (the collision of two EH) is caused by the two-dimensional (one-dimensional) set of the endpoints. In the present article, we examine the stability of the topology of the EH. We see that a simple case of a single spherical EH is unstable. Furthermore, in general, an EH with handles (a torus, a double torus, ...) is structurally stable in the sense of catastrophe theory.Comment: 21 pages, revtex, five figures containe

The Asymmetric Merger of Black Holes

We study event horizons of non-axisymmetric black holes and show how features found in axisymmetric studies of colliding black holes and of toroidal black holes are non-generic and how new features emerge. Most of the details of black hole formation and black hole merger are known only in the axisymmetric case, in which numerical evolution has successfully produced dynamical space-times. The work that is presented here uses a new approach to construct the geometry of the event horizon, not by locating it in a given spacetime, but by direct construction. In the axisymmetric case, our method produces the familiar pair-of-pants structure found in previous numerical simulations of black hole mergers, as well as event horizons that go through a toroidal epoch as discovered in the collapse of rotating matter. The main purpose of this paper is to show how new - substantially different - features emerge in the non-axisymmetric case. In particular, we show how black holes generically go through a toroidal phase before they become spherical, and how this fits together with the merger of black holes.Comment: 28 pages, 10 figures, uses REVTEX. Improved quality figures and additional color images are provided at http://www.phyast.pitt.edu/~shusa/EH

Generalized Weyl Solutions

It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyl's construction is generalized here to arbitrary dimension $D\ge 4$. The general solution of the D-dimensional vacuum Einstein equations that admits D-2 orthogonal commuting non-null Killing vector fields is given either in terms of D-3 independent axisymmetric solutions of Laplace's equation in three-dimensional flat space or by D-4 independent solutions of Laplace's equation in two-dimensional flat space. Explicit examples of new solutions are given. These include a five-dimensional asymptotically flat ``black ring'' with an event horizon of topology S^1 x S^2 held in equilibrium by a conical singularity in the form of a disc.Comment: 50 pages, 10 figures; v2: minor improvement

Insights into Eyestalk Ablation Mechanism to Induce Ovarian Maturation in the Black Tiger Shrimp

Eyestalk ablation is commonly practiced in crustacean to induce ovarian maturation in captivity. The molecular mechanism of the ablation has not been well understood, preventing a search for alternative measures to induce ovarian maturation in aquaculture. This is the first study to employ cDNA microarray to examine effects of eyestalk ablation at the transcriptomic level and pathway mapping analysis to identify potentially affected biological pathways in the black tiger shrimp (Penaeus monodon). Microarray analysis comparing between gene expression levels of ovaries from eyestalk-intact and eyestalk-ablated brooders revealed 682 differentially expressed transcripts. Based on Hierarchical clustering of gene expression patterns, Gene Ontology annotation, and relevant functions of these differentially expressed genes, several gene groups were further examined by pathway mapping analysis. Reverse-transcriptase quantitative PCR analysis for some representative transcripts confirmed microarray data. Known reproductive genes involved in vitellogenesis were dramatically increased during the ablation. Besides these transcripts expected to be induced by the ablation, transcripts whose functions involved in electron transfer mechanism, immune responses and calcium signal transduction were significantly altered following the ablation. Pathway mapping analysis revealed that the activation of gonadotropin-releasing hormone signaling, calcium signaling, and progesterone-mediated oocyte maturation pathways were putatively crucial to ovarian maturation induced by the ablation. These findings shed light on several possible molecular mechanisms of the eyestalk ablation effect and allow more focused investigation for an ultimate goal of finding alternative methods to replace the undesirable practice of the eyestalk ablation in the future