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