Spherically Symmetric Gravitational Collapse of Perfect Fluids

Formulating a perfect fluid filled spherically symmetric metric utilizing the 3+1 formalism for general relativity, we show that the metric coefficients are completely determined by the mass-energy distribution, and its time rate of change on an initial spacelike hypersurface. Rather than specifying Schwarzschild coordinates for the exterior of the collapsing region, we let the interior dictate the form of the solution in the exterior, and thus both regions are found to be written in one coordinate patch. This not only alleviates the need for complicated matching schemes at the interface, but also finds a new coordinate system for the Schwarzschild spacetime expressed in generalized Painleve-Gullstrand coordinates.Comment: 3 pages, To appear in the proceedings of the eleventh Marcel Grossmann meeting on general relativity (MGXI), 23-29 July, 2006, Berli

SSB-1 of the yeast Saccharomyces cerevisiae is a nucleolar-specific, silver-binding protein that is associated with the snR10 and snR11 small nuclear RNAs

SSB-1, the yeast single-strand RNA-binding protein, is demonstrated to be a yeast nucleolar-specific, silver-binding protein. In double-label immunofluorescence microscopy experiments antibodies to two other nucleolar proteins, RNA Pol I 190-kD and fibrillarin, were used to reveal the site of rRNA transcription; i.e., the fibrillar region of the nucleolus. SSB-1 colocalized with fibrillarin in a double-label immunofluorescence mapping experiment to the yeast nucleolus. SSB-1 is located, though, over a wider region of the nucleolus than the transcription site marker. Immunoprecipitations of yeast cell extracts with the SSB-1 antibody reveal that in 150 mM NaCl SSB-1 is bound to two small nuclear RNAs (snRNAs). These yeast snRNAs are snR10 and snR11, with snR10 being predominant. Since snR10 has been implicated in pre-rRNA processing, the association of SSB-1 and snR10 into a nucleolar snRNP particle indicates SSB-1 involvement in rRNA processing as well. Also, another yeast protein, SSB-36-kD, isolated by single- strand DNA chromatography, is shown to bind silver under the conditions used for nucleolar-specific staining. It is, most likely, another yeast nucleolar protein

Bose-Einstein Condensates with Large Number of Vortices

We show that as the number of vortices in a three dimensional Bose-Einstein Condensate increases, the system reaches a "quantum Hall" regime where the density profile is a Gaussian in the xy-plane and an inverted parabolic profile along z. The angular momentum of the system increases as the vortex lattice shrinks. However, Coriolis force prevents the unit cell of the vortex lattice from shrinking beyond a minimum size. Although the recent MIT experiment is not exactly in the quantum Hall regime, it is close enough for the present results to be used as a guide. The quantum Hall regime can be easily reached by moderate changes of the current experimental parameters.Comment: 4 pages, no figure

1+1+2 Electromagnetic perturbations on general LRS space-times: Regge-Wheeler and Bardeen-Press equations

We use the, covariant and gauge-invariant, 1+1+2 formalism developed by Clarkson and Barrett, and develop new techniques, to decouple electromagnetic (EM) perturbations on arbitrary locally rotationally symmetric (LRS) space-times. Ultimately, we derive 3 decoupled complex equations governing 3 complex scalars. One of these is a new Regge-Wheeler (RW) equation generalized for LRS space-times, whereas the remaining two are new generalizations of the Bardeen-Press (BP) equations. This is achieved by first using linear algebra techniques to rewrite the first-order Maxwell equations in a new complex 1+1+2 form which is conducive to decoupling. This new complex system immediately yields the generalized RW equation, and furthermore, we also derive a decoupled equation governing a newly defined complex EM 2-vector. Subsequently, a further decomposition of the 1+1+2 formalism into a 1+1+1+1 formalism is developed, allowing us to decompose the complex EM 2-vector, and its governing equations, into spin-weighted scalars, giving rise to the generalized BP equations