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

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 $5D$ 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 $5D$, 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.

Late time cosmic acceleration from vacuum Brans-Dicke theory in 5D

We show that the scalar-vacuum Brans-Dicke equations in 5D are equivalent to Brans-Dicke theory in 4D with a self interacting potential and an effective matter field. The cosmological implication, in the context of FRW models, is that the observed accelerated expansion of the universe comes naturally from the condition that the scalar field is not a ghost, i.e., $\omega > - 3/2$. We find an effective matter-dominated 4D universe which shows accelerated expansion if $- 3/2 < \omega < - 1$. We study the question of whether accelerated expansion can be made compatible with large values of $\omega$, within the framework of a 5D scalar-vacuum Brans-Dicke theory with variable, instead of constant, parameter $\omega$. In this framework, and based on a general class of solutions of the field equations, we demonstrate that accelerated expansion is incompatible with large values of $\omega$.Comment: In V2 the summary section is expanded. To be published in Classical and Quantum Gravity

The principle of least action for test particles in a four-dimensional spacetime embedded in 5D

It is well known that, in the five-dimensional scenario of braneworld and space-time-mass theories, geodesic motion in 5D is observed to be non-geodesic in 4D. Usually, the discussion is purely geometric and based on the dimensional reduction of the geodesic equation in 5D, without any reference to the test particle whatsoever. In this work we obtain the equation of motion in 4D directly from the principle of least action. So our main thrust is not the geometry but the particle observed in 4D. A clear physical picture emerges from our work. Specifically, that the deviation from the geodesic motion in 4D is due to the variation of the rest mass of a particle, which is induced by the scalar field in the 5D metric and the explicit dependence of the spacetime metric on the extra coordinate. Thus, the principle of least action not only leads to the correct equations of motion, but also provides a concrete physical meaning for a number of algebraic quantities appearing in the geometrical reduction of the geodesic equation

The Big Bang as a Phase Transition

We study a five-dimensional cosmological model, which suggests that the universe bagan as a discontinuity in a (Higgs-type) scalar field, or alternatively as a conventional four-dimensional phase transition.Comment: 10 pages, 2 figures; typo corrected in equation (18); 1 reference added; version to appear in International Journal of Modern Physics

The internal structure and formation of early-type galaxies: the gravitational--lens system MG2016+112 at z=1.004

[Abridged] We combine our measurements of the velocity dispersion and the surface brightness profile of the lens galaxy D in the system MG2016+112 (z=1.004) with constraints from gravitational lensing to study its internal mass distribution. We find that: (i) dark matter accounts for >50% of the total mass within the Einstein radius (99% CL), excluding at the 8-sigma level that mass follows light inside the Einstein radius with a constant mass-to-light ratio (M/L). (ii) the total mass distribution inside the Einstein radius is well-described by a density profile ~r^-gamma' with an effective slope gamma'=2.0+-0.1+-0.1, including random and systematic uncertainties. (iii) The offset of galaxy D from the local Fundamental Plane independently constrains the stellar M/L, and matches the range derived from our models, leading to a more stringent lower limit of >60% on the fraction of dark matter within the Einstein radius (99%CL). Under the assumption of adiabatic contraction, the inner slope of the dark matter halo before the baryons collapsed is gamma_i<1.4 (68 CL), marginally consistent with the highest-resolution cold dark matter simulations that indicate gamma_i~1.5. This might indicate that either adiabatic contraction is a poor description of E/S0 formation or that additional processes play a role as well. Indeed, the apparently isothermal density distribution inside the Einstein radius, is not a natural outcome of adiabatic contraction models, where it appears to be a mere coincidence. By contrast, we argue that isothermality might be the result of a stronger coupling between luminous and dark-matter, possibly the result of (incomplete) violent relaxation processes. Hence, we conclude that galaxy D appears already relaxed 8 Gyr ago.Comment: 8 pages, 4 figures, ApJ, in press, minor change

Distribution of Manganese in a Bio-Topo Sequence of Southeastern Iowa Soils

Manganese extractable by sodium hydrosulfite was determined for 9 soil profiles of a bio-topo (vegetation and drainage) sequence in southeastern Iowa. The distribution of manganese in the soils studied is influenced by vegetation, drainage, and pH. Under prairie vegetation the manganese is evenly distributed with depth in the well-drained soil, but with increasing wetness of the soil profile, manganese is apparently lost from the A1 horizon and accumulates in the lower part of the B horizon. Manganese accumulates in the A1 and A2 horizons of the well-drained soils developed under forest vegetation, but in profiles of increasing wetness the amount of manganese in the A1 and A2 horizons decreases and the amount of manganese in the lower B horizon increases. The distribution of manganese in the transition prairie forest soils was intermediate between soils developed under prairie vegetation and those developed under forest vegetation

Effective spacetime from multi-dimensional gravity

We study the effective spacetimes in lower dimensions that can be extracted from a multidimensional generalization of the Schwarzschild-Tangherlini spacetimes derived by Fadeev, Ivashchuk and Melnikov ({\it Phys. Lett,} {\bf A 161} (1991) 98). The higher-dimensional spacetime has $D = (4 + n + m)$ dimensions, where $n$ and $m$ are the number of "internal" and "external" extra dimensions, respectively. We analyze the effective $(4 + n)$ spacetime obtained after dimensional reduction of the $m$ external dimensions. We find that when the $m$ extra dimensions are compact (i) the physics in lower dimensions is independent of $m$ and the character of the singularities in higher dimensions, and (ii) the total gravitational mass $M$ of the effective matter distribution is less than the Schwarzshild mass. In contrast, when the $m$ extra dimensions are large this is not so; the physics in $(4 + n)$ does explicitly depend on $m$, as well as on the nature of the singularities in high dimensions, and the mass of the effective matter distribution (with the exception of wormhole-like distributions) is bigger than the Schwarzshild mass. These results may be relevant to observations for an experimental/observational test of the theory.Comment: A typo in Eq. (24) is fixe

Active gravitational mass and the invariant characterization of Reissner-Nordstrom spacetime

We analyse the concept of active gravitational mass for Reissner-Nordstrom spacetime in terms of scalar polynomial invariants and the Karlhede classification. We show that while the Kretschmann scalar does not produce the expected expression for the active gravitational mass, both scalar polynomial invariants formed from the Weyl tensor, and the Cartan scalars, do.Comment: 6 pages Latex, to appear in General Relativity and Gravitatio