Multidimensional perfect fluid cosmology with stable compactified internal dimensions

Multidimensional cosmological models in the presence of a bare cosmological constant and a perfect fluid are investigated under dimensional reduction to 4-dimensional effective models. Stable compactification of the internal spaces is achieved for a special class of perfect fluids. The external space behaves in accordance with the standard Friedmann model. Necessary restrictions on the parameters of the models are found to ensure dynamical behavior of the external (our) universe in agreement with observations.Comment: 11 pages, Latex2e, uses IOP packages, submitted to Class.Quant.Gra

Classification and Moduli Kahler Potentials of G_2 Manifolds

Compact manifolds of G_2 holonomy may be constructed by dividing a seven-torus by some discrete symmetry group and then blowing up the singularities of the resulting orbifold. We classify possible group elements that may be used in this construction and use this classification to find a set of possible orbifold groups. We then derive the moduli Kahler potential for M-theory on the resulting class of G_2 manifolds with blown up co-dimension four singularities.Comment: 30 pages, Latex, references adde

G_2 Domain Walls in M-theory

M-theory is considered in its low-energy limit on a G_2 manifold with non-vanishing flux. Using the Killing spinor equations for linear flux, an explicit set of first-order bosonic equations for supersymmetric solutions is found. These solutions describe a warped product of a domain wall in four-dimensional space-time and a deformed G_2 manifold. It is shown how these domain walls arise from the perspective of the associated four-dimensional N=1 effective supergravity theories. We also discuss the inclusion of membrane and M5-brane sources.Comment: 30 pages, Late

Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multi-component, curvature, and rotation

We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a flat background coincide exactly with the ones known in Newton's theory. Here, we present the general relativistic second-order correction terms arising due to (i) pressure, (ii) multi-component, (iii) background curvature, and (iv) rotation. In case of multi-component zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic result again coincides with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background curvature, or rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order. In the small-scale limit (far inside the horizon), relativistic equations including the rotation coincide with the ones in Newton's gravity.Comment: 41 pages, no figur

A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models

Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently regained interest as a good fit to the observed cosmic microwave background temperature fluctuations. However, it is generally thought that a globally, exactly-flat FLRW model is theoretically improbable. Here, in order to obtain a probability space on the set F of compact, comoving, 3-spatial sections of FLRW models, a physically motivated hypothesis is proposed, using the density parameter Omega as a derived rather than fundamental parameter. We assume that the processes that select the 3-manifold also select a global mass-energy and a Hubble parameter. The inferred range in Omega consists of a single real value for any 3-manifold. Thus, the obvious measure over F is the discrete measure. Hence, if the global mass-energy and Hubble parameter are a function of 3-manifold choice among compact FLRW models, then probability spaces parametrised by Omega do not, in general, give a zero probability of a flat model. Alternatively, parametrisation by the injectivity radius r_inj ("size") suggests the Lebesgue measure. In this case, the probability space over the injectivity radius implies that flat models occur almost surely (a.s.), in the sense of probability theory, and non-flat models a.s. do not occur.Comment: 19 pages, 4 figures; v2: minor language improvements; v3: generalisation: m, H functions of

Gaussian coordinate systems for the Kerr metric

We present the whole class of Gaussian coordinate systems for the Kerr metric. This is achieved through the uses of the relationship between Gaussian observers and the relativistic Hamilton-Jacobi equation. We analyze the completeness of this coordinate system. In the appendix we present the equivalent JEK formulation of General Relativity -- the so-called quasi-Maxwellian equations -- which acquires a simpler form in the Gaussian coordinate system. We show how this set of equations can be used to obtain the internal metric of the Schwazschild solution, as a simple example. We suggest that this path can be followed to the search of the internal Kerr metric