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

Who Helps Public Schools? Public Education Support Organizations in 2010

There were more than 19,000 nonprofit organizations devoted to supporting public education in the United States in 2007. These organizations include booster clubs, parent-teacher groups, public education funds, scholarship funds, high school alumni associations, and others. While most of these organizations are small, together they spent roughly $4.3 billion in support of public education in 2007.This report assesses the current status of education support organizations in the United States; provides details on the activities, capacities, and resources of public education funds; and compares Public Education Network (PEN) member organizations with other types of education funds. On the basis of a survey of public education funds and an analysis of the latest data available from the National Center for Charitable Statistics, the report identifies key similarities and differences among the groups.Public education funds are dedicated to assisting public schools and school districts by raising money to support programs for teacher training and support, after-school programs, and school supplies and by promoting community support for public schools. The project was commissioned by PEN in Washington, D.C

Equivalence Between Space-Time-Matter and Brane-World Theories

We study the relationship between space-time-matter (STM) and brane theories. These two theories look very different at first sight, and have different motivation for the introduction of a large extra dimension. However, we show that they are equivalent to each other. First we demonstrate that STM predicts local and non-local high-energy corrections to general relativity in 4D, which are identical to those predicted by brane-world models. Secondly, we notice that in brane models the usual matter in 4D is a consequence of the dependence of five-dimensional metrics on the extra coordinate. If the 5D bulk metric is independent of the extra dimension, then the brane is void of matter. Thus, in brane theory matter and geometry are unified, which is exactly the paradigm proposed in STM. Consequently, these two 5D theories share the same concepts and predict the same physics. This is important not only from a theoretical point of view, but also in practice. We propose to use a combination of both methods to alleviate the difficult task of finding solutions on the brane. We show an explicit example that illustrate the feasibility of our proposal.Comment: Typos corrected, three references added. To appear in Mod. Phys. Let

Human Service Nonprofits and Government Collaboration: Findings from the 2010 National Survey of Nonprofit Government Contracting and Grants

Presents nonprofit survey results on government contracts; their share of revenue; problems, including late or partial payments, complex application and reporting processes, and changes to contract terms; how nonprofits cope with them; and the results

Agents of Place: Negotiations between Artist and Government in Philippine Public Art

The paper inquires into public art produced by artists and government authorities. It interprets collaboration as a site of negotiating various interests; holding possibilities for both disruption and complicity; antagonism and amelioration. The research considers two art projects in the Philippine context: first; the Paoay sand dunes sculpture park made between 2012 and 2015 in the Northern Ilocos region; and second; the ongoing Pasig River Art for Urban Change; beginning with Bakawan in 2015 in the Philippine capital Metro Manila. As both involve the artist Leeroy New (b. 1986) working with different government agencies; the paper tracks inconspicuous shifts not only in ways of working; but also in how the works and the sites themselves are conceived. The two physical sites; the sand dunes and the river; are both natural formations whose sensuous presence has been evoked in other cultural texts and forms of speech. The research examines how governmental imagination and artistic agency work to negotiate readings of place. How does the artist thicken such readings; and complicate the essentialist view of place that banks on heritage? This analysis draws from discourses on public art and collaboration; and it places New’s work in dialogue with historical precedents in Philippine experimental art and site-specific practices; as well as cultural texts such as Ishmael Bernal’s Himala

Self-similar cosmologies in 5D: spatially flat anisotropic models

In the context of theories of Kaluza-Klein type, with a large extra dimension, we study self-similar cosmological models in 5D that are homogeneous, anisotropic and spatially flat. The "ladder" to go between the physics in 5D and 4D is provided by Campbell-Maagard's embedding theorems. We show that the 5-dimensional field equations $R_{AB} = 0$ determine the form of the similarity variable. There are three different possibilities: homothetic, conformal and "wave-like" solutions in 5D. We derive the most general homothetic and conformal solutions to the 5D field equations. They require the extra dimension to be spacelike, and are given in terms of one arbitrary function of the similarity variable and three parameters. The Riemann tensor in 5D is not zero, except in the isotropic limit, which corresponds to the case where the parameters are equal to each other. The solutions can be used as 5D embeddings for a great variety of 4D homogeneous cosmological models, with and without matter, including the Kasner universe. Since the extra dimension is spacelike, the 5D solutions are invariant under the exchange of spatial coordinates. Therefore they also embed a family of spatially {\it inhomogeneous} models in 4D. We show that these models can be interpreted as vacuum solutions in braneworld theory. Our work (I) generalizes the 5D embeddings used for the FLRW models; (II) shows that anisotropic cosmologies are, in general, curved in 5D, in contrast with FLRW models which can always be embedded in a 5D Riemann-flat (Minkowski) manifold; (III) reveals that anisotropic cosmologies can be curved and devoid of matter, both in 5D and 4D, even when the metric in 5D explicitly depends on the extra coordinate, which is quite different from the isotropic case.Comment: Typos corrected. Minor editorial changes and additions in the Introduction and Summary section

Brane world solutions of perfect fluid in the background of a bulk containing dust or cosmological constant

The paper presents some solutions to the five dimensional Einstein equations due to a perfect fluid on the brane with pure dust filling the entire bulk in one case and a cosmological constant (or vacuum) in the bulk for the second case. In the first case, there is a linear relationship between isotropic pressure, energy density and the brane tension, while in the second case, the perfect fluid is assumed to be in the form of chaplygin gas. Cosmological solutions are found both for brane and bulk scenarios and some interesting features are obtained for the chaplygin gas on the brane which are distinctly different from the standard cosmology in four dimensions.Comment: 10 Latex pages, 5 figure