8,090 research outputs found
Wave-like Solutions for Bianchi type-I cosmologies in 5D
We derive exact solutions to the vacuum Einstein field equations in 5D, under
the assumption that (i) the line element in 5D possesses self-similar symmetry,
in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the
metric tensor is diagonal and independent of the coordinates for ordinary 3D
space. These assumptions lead to three different types of self-similarity in
5D: homothetic, conformal and "wave-like". In this work we present the most
general wave-like solutions to the 5D field equations. Using the standard
technique based on Campbell's theorem, they generate a large number of
anisotropic cosmological models of Bianchi type-I, which can be applied to our
universe after the big-bang, when anisotropies could have played an important
role. We present a complete review of all possible cases of self-similar
anisotropic cosmologies in 5D. Our analysis extends a number of previous
studies on wave-like solutions in 5D with spatial spherical symmetry
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
Institutional Goal Priorities in Texas: A Look at an Associate Degree Nursing Program
Trends indicate that Texans will enter community colleges seeking the skills and competencies needed to survive in today’s highly technical work environments. Nursing and allied health occupations are expected to account for 54,500 of the projected 10.3 million jobs avaiIable in the Texas workforce in the year 2000. The educational trend prompted by the need for a quality workforce in Texas mandates that community colleges establish institutional goal priorities among major constituent groups to maintain program effectiveness. This study examined the current and preferred importance of institutional goals among four community college associate degree nursing constituent groups: advisory board members, college administrators, faculty, and final semester students
The genus Nacobbus Thorne and Allen, 1944 in Argentina : 2. Association between N. aberrans (Thorne, 1935) Thorne and Allen, 1944 and the weed Sisymbrium irio L.
Levi-Civita spacetimes in multidimensional theories
We obtain the most general static cylindrically symmetric vacuum solutions of
the Einstein field equations in dimensions. Under the assumption of
separation of variables, we construct a family of Levi-Civita-Kasner vacuum
solutions in . We discuss the dimensional reduction of the static
solutions. Depending on the reduction procedure, they can be interpreted either
as a scalar-vacuum generalization of Levi-Civita spacetimes, or as the
effective 4D vacuum spacetime outside of an idealized string in braneworld
theory.Comment: 7 pages. Accepted for publication in Mod. Phys. Lett. A (MPLA
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
An exact self-similar solution for an expanding ball of radiation
We give an exact solution of the Einstein equations which in 4D can be
interpreted as a spherically symmetric dissipative distribution of matter, with
heat flux, whose effective density and pressure are nonstatic, nonuniform, and
satisfy the equation of state of radiation. The matter satisfies the usual
energy and thermodynamic conditions. The energy density and temperature are
related by the Stefan-Boltzmann law. The solution admits a homothetic Killing
vector in , which induces the existence of self-similar symmetry in 4D,
where the line element as well as the dimensionless matter quantities are
invariant under a simple "scaling" group.Comment: New version expanded and improved. To appear in Int. J. Mod. Phys.
Exterior spacetime for stellar models in 5-dimensional Kaluza-Klein gravity
It is well-known that Birkhoff's theorem is no longer valid in theories with
more than four dimensions. Thus, in these theories the effective 4-dimensional
picture allows the existence of different possible, non-Schwarzschild,
scenarios for the description of the spacetime outside of a spherical star,
contrary to general relativity in 4D. We investigate the exterior spacetime of
a spherically symmetric star in the context of Kaluza-Klein gravity. We take a
well-known family of static spherically symmetric solutions of the Einstein
equations in an empty five-dimensional universe, and analyze possible stellar
exteriors that are conformal to the metric induced on four-dimensional
hypersurfaces orthogonal to the extra dimension. All these exteriors are
continuously matched with the interior of the star. Then, without making any
assumptions about the interior solution, we prove the following statement: the
condition that in the weak-field limit we recover the usual Newtonian physics
singles out an unique exterior. This exterior is "similar" to Scharzschild
vacuum in the sense that it has no effect on gravitational interactions.
However, it is more realistic because instead of being absolutely empty, it is
consistent with the existence of quantum zero-point fields. We also examine the
question of how would the deviation from the Schwarzschild vacuum exterior
affect the parameters of a neutron star. In the context of a model star of
uniform density, we show that the general relativity upper limit M/R < 4/9 is
significantly increased as we go away from the Schwarzschild vacuum exterior.
We find that, in principle, the compactness limit of a star can be larger than
1/2, without being a black hole. The generality of our approach is also
discussed.Comment: Typos corrected. Accepted for publication in Classical and Quantum
Gravit
Computational approach to the Schottky problem
We present a computational approach to the classical Schottky problem based
on Fay's trisecant identity for genus . For a given Riemann matrix
, the Fay identity establishes linear dependence
of secants in the Kummer variety if and only if the Riemann matrix corresponds
to a Jacobian variety as shown by Krichever. The theta functions in terms of
which these secants are expressed depend on the Abel maps of four arbitrary
points on a Riemann surface. However, there is no concept of an Abel map for
general . To establish linear dependence of the
secants, four components of the vectors entering the theta functions can be
chosen freely. The remaining components are determined by a Newton iteration to
minimize the residual of the Fay identity. Krichever's theorem assures that if
this residual vanishes within the finite numerical precision for a generic
choice of input data, then the Riemann matrix is with this numerical precision
the period matrix of a Riemann surface. The algorithm is compared in genus 4
for some examples to the Schottky-Igusa modular form, known to give the Jacobi
locus in this case. It is shown that the same residuals are achieved by the
Schottky-Igusa form and the approach based on the Fay identity in this case. In
genera 5, 6 and 7, we discuss known examples of Riemann matrices and
perturbations thereof for which the Fay identity is not satisfied
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