Hydrostatic Equilibrium of a Perfect Fluid Sphere with Exterior Higher-Dimensional Schwarzschild Spacetime

We discuss the question of how the number of dimensions of space and time can influence the equilibrium configurations of stars. We find that dimensionality does increase the effect of mass but not the contribution of the pressure, which is the same in any dimension. In the presence of a (positive) cosmological constant the condition of hydrostatic equilibrium imposes a lower limit on mass and matter density. We show how this limit depends on the number of dimensions and suggest that $\Lambda > 0$ is more effective in 4D than in higher dimensions. We obtain a general limit for the degree of compactification (gravitational potential on the boundary) of perfect fluid stars in $D$-dimensions. We argue that the effects of gravity are stronger in 4D than in any other number of dimensions. The generality of the results is also discussed

Leibniz algebroid associated with a Nambu-Poisson structure

The notion of Leibniz algebroid is introduced, and it is shown that each Nambu-Poisson manifold has associated a canonical Leibniz algebroid. This fact permits to define the modular class of a Nambu-Poisson manifold as an appropiate cohomology class, extending the well-known modular class of Poisson manifolds

A new geometric setting for classical field theories

A new geometrical setting for classical field theories is introduced. This description is strongly inspired in the one due to Skinner and Rusk for singular lagrangians systems. For a singular field theory a constraint algorithm is developed that gives a final constraint submanifold where a well-defined dynamics exists. The main advantage of this algorithm is that the second order condition is automatically included.Comment: 22 page

Stellar models with Schwarzschild and non-Schwarzschild vacuum exteriors

A striking characteristic of non-Schwarzschild vacuum exteriors is that they contain not only the total gravitational mass of the source, but also an {\it arbitrary} constant. In this work, we show that the constants appearing in the "temporal Schwarzschild", "spatial Schwarzschild" and "Reissner-Nordstr{\"o}m-like" exteriors are not arbitrary but are completely determined by star's parameters, like the equation of state and the gravitational potential. Consequently, in the braneworld scenario the gravitational field outside of a star is no longer determined by the total mass alone, but also depends on the details of the internal structure of the source. We show that the general relativistic upper bound on the gravitational potential $M/R < 4/9$, for perfect fluid stars, is significantly increased in these exteriors. Namely, $M/R < 1/2$, $M/R < 2/3$ and $M/R < 1$ for the temporal Schwarzschild, spatial Schwarzschild and Reissner-Nordstr{\"o}m-like exteriors, respectively. Regarding the surface gravitational redshift, we find that the general relativistic Schwarzschild exterior as well as the braneworld spatial Schwarzschild exterior lead to the same upper bound, viz., $Z < 2$. However, when the external spacetime is the temporal Schwarzschild metric or the Reissner-Nordstr{\"o}m-like exterior there is no such constraint: $Z < \infty$. This infinite difference in the limiting value of $Z$ is because for these exteriors the effective pressure at the surface is negative. The results of our work are potentially observable and can be used to test the theory.Comment: 19 pages, 3 figures and caption

A 22 Degree Tidal Tail for Palomar 5

Using Data Release 4 of the Sloan Digital Sky Survey, we have applied an optimal contrast, matched filter technique to trace the trailing tidal tail of the globular cluster Palomar 5 to a distance of 18.5 degrees from the center of the cluster. This more than doubles the total known length of the tail to some 22 degrees on the sky. Based on a simple model of the Galaxy, we find that the stream's orientation on the sky is consistent at the 1.7 sigma level with existing proper motion measurements. We find that a spherical Galactic halo is adequate to model the stream over its currently known length, and we are able to place new constraints on the current space motion of the cluster.Comment: 10 pages, 3 figures, accepted for publication in ApJ Letter

Radiative corrections to the three-body region of the Dalitz plot of baryon semileptonic decays with angular correlation between polarized emitted baryons and charged leptons: The initial-baryon rest frame case

We complement the results for the radiative corrections to the s2.l angular correlation of baryon semileptonic decays of Ref. [1] with the final results in the rest frame of the decaying baryon.Comment: 7 pages, Revtex4, no figure

Metabolic profiling reveals coordinated switches in primary carbohydrate metabolism in grape berry (Vitis vinifera L.), a non-climacteric fleshy fruit

Changes in carbohydrate metabolism during grape berry development play a central role in shaping the final composition of the fruit. The present work aimed to identify metabolic switches during grape development and to provide insights into the timing of developmental regulation of carbohydrate metabolism. Metabolites from central carbon metabolism were measured using high-pressure anion-exchange chromatography coupled to tandem mass spectrometry and enzymatic assays during the development of grape berries from either field-grown vines or fruiting cuttings grown in the greenhouse. Principal component analysis readily discriminated the various stages of berry development, with similar trajectories for field-grown and greenhouse samples. This showed that each stage of fruit development had a characteristic metabolic profile and provided compelling evidence that the fruit-bearing cuttings are a useful model system to investigate regulation of central carbon metabolism in grape berry. The metabolites measured showed tight coordination within their respective pathways, clustering into sugars and sugar-phosphate metabolism, glycolysis, and the tricarboxylic acid cycle. In addition, there was a pronounced shift in metabolism around veraison, characterized by rapidly increasing sugar levels and decreasing organic acids. In contrast, glycolytic intermediates and sugar phosphates declined before veraison but remained fairly stable post-veraison. In summary, these detailed and comprehensive metabolite analyses revealed the timing of important switches in primary carbohydrate metabolism, which could be related to transcriptional and developmental changes within the berry to achieve an integrated understanding of grape berry development. The results are discussed in a meta-analysis comparing metabolic changes in climacteric versus non-climacteric fleshy fruits