Generating Anisotropic Collapse and Expansion Solutions of Einstein's Equations

Analytic gravitational collapse and expansion solutions with anisotropic pressure are generated. Metric functions are found by requiring zero heat flow scalar. It emerges that a single function generates the anisotropic solutions. Each generating function contains an arbitrary function of time which can be chosen to fit various astrophysical time profiles. Two examples are provided: a bounded collapse metric and an expanding cosmological solutionComment: to appear in Gen. Rel. Gravi

Killing-Yano tensors in spaces admitting a hypersurface orthogonal Killing vector

Methods are presented for finding Killing-Yano tensors, conformal Killing-Yano tensors, and conformal Killing vectors in spacetimes with a hypersurface orthogonal Killing vector. These methods are similar to a method developed by the authors for finding Killing tensors. In all cases one decomposes both the tensor and the equation it satisfies into pieces along the Killing vector and pieces orthogonal to the Killing vector. Solving the separate equations that result from this decomposition requires less computing than integrating the original equation. In each case, examples are given to illustrate the method

From Taub Numbers to the Bondi Mass

Taub numbers are studied on asymptotically flat backgrounds with Killing symmetries. When the field equations are solved for a background spacetime and higher order functional derivatives (higher order variational derivatives of the Hilbert Lagrangean) are solved for perturbations from the background, such perturbed space-times admit zeroth, first, and second order Taub numbers. Zeroth order Taub numbers are Komar constants (upto numerical factors) or Penrose-Goldberg constants of the background. For a Killing symmetry of the background, first order Taub numbers give the contribution of the linearized perturbation to the associated backgound quantity, such as the perturbing mass. Second order Taub numbers give the contribution of second order perturbations to the background quantity. The Bondi mass is a sum of first and second order Taubs numbers on a Minkowski background.Comment: To appear in the proceedings of the 8th Marcel Grossmann Conferenc

A Spacetime in Toroidal Coordinates

We present an exact solution of Einstein's field equations in toroidal coordinates. The solution has three regions: an interior with a string equation of state; an Israel boundary layer; an exterior with constant isotropic pressure and constant density, locally isometric to anti-de Sitter spacetime. The exterior can be a cosmological vacuum with negative cosmological constant. The size and mass of the toroidal loop depend on the size of the cosmological constant.Comment: to appear in J. Math. Phy

Analysis of a conserved cellulase transcriptional regulator reveals inducer-independent production of cellulolytic enzymes in Neurospora crassa.

Cellulose is recalcitrant to deconstruction to glucose for use in fermentation strategies for biofuels and chemicals derived from lignocellulose. In Neurospora crassa, the transcriptional regulator, CLR-2, is required for cellulolytic gene expression and cellulose deconstruction. To assess conservation and divergence of cellulase gene regulation between fungi from different ecological niches, we compared clr-2 function with its ortholog (clrB) in the distantly related species, Aspergillus nidulans. Transcriptional profiles induced by exposure to crystalline cellulose were similar in both species. Approximately 50% of the cellulose-responsive genes showed strict dependence on functional clr-2/clrB, with a subset of 28 genes encoding plant biomass degrading enzymes that were conserved between N. crassa and A. nidulans. Importantly, misexpression of clr-2 under noninducing conditions was sufficient to drive cellulase gene expression, secretion, and activity in N. crassa, to a level comparable to wild type exposed to Avicel. However, misexpression of clrB in A. nidulans was not sufficient to drive cellulase gene expression under noninducing conditions, although an increase in cellulase activity was observed under crystalline cellulose conditions. Manipulation of clr-2 orthologs among filamentous fungi may enable regulated cellulosic enzyme production in a wide array of culture conditions and host strains, potentially reducing costs associated with enzyme production for plant cell wall deconstruction. However, this functionality may require additional engineering in some species

Fractional Boundaries for Fluid Spheres

A single Israel layer can be created when two metrics adjoin with no continuous metric derivative across the boundary. The properties of the layer depend only on the two metrics it separates. By using a fractional derivative match, a family of Israel layers can be created between the same two metrics. The family is indexed by the order of the fractional derivative. The method is applied to Tolman IV and V interiors and a Schwarzschild vacuum exterior. The method creates new ranges of modeling parameters for fluid spheres. A thin shell analysis clarifies pressure/tension in the family of boundary layers.Comment: to appear in J. Math. Phy

A Conserved Bach Current

The Bach tensor and a vector which generates conformal symmetries allow a conserved four-current to be defined. The Bach four-current gives rise to a quasilocal two-surface expression for power per luminosity distance in the Vaidya exterior of collapsing fluid interiors. This is interpreted in terms of entropy generation.Comment: to appear in Class. Quantum Gra

Scale Symmetries of Spherical String Fluids

We consider homothetic maps in a family of spherical relativistic star models. A generalization of Vaidya's radiating metric provides a fluid atmosphere of radiation and strings. The similarity structure of the string fluid is investigated.Comment: to appear in J. Math. Physic

Energy Transport in the Vaidya System

Energy transport mechanisms can be generated by imposing relations between null tetrad Ricci components. Several kinds of mass and density transport generated by these relations are studied for the generalized Vaidya system.Comment: J.Math. Phys. (to appear