Newtonian and Post-Newtonian approximations of the k = 0 Friedmann Robertson Walker Cosmology

In a previous paper we derived a post-Newtonian approximation to cosmology which, in contrast to former Newtonian and post-Newtonian cosmological theories, has a well-posed initial value problem. In this paper, this new post-Newtonian theory is compared with the fully general relativistic theory, in the context of the k = 0 Friedmann Robertson Walker cosmologies. It is found that the post-Newtonian theory reproduces the results of its general relativistic counterpart, whilst the Newtonian theory does not.Comment: 11 pages, Latex, corrected typo

Post-Newtonian Cosmology

Newtonian Cosmology is commonly used in astrophysical problems, because of its obvious simplicity when compared with general relativity. However it has inherent difficulties, the most obvious of which is the non-existence of a well-posed initial value problem. In this paper we investigate how far these problems are met by using the post-Newtonian approximation in cosmology.Comment: 12 pages, Late

Integrability of irrotational silent cosmological models

We revisit the issue of integrability conditions for the irrotational silent cosmological models. We formulate the problem both in 1+3 covariant and 1+3 orthonormal frame notation, and show there exists a series of constraint equations that need to be satisfied. These conditions hold identically for FLRW-linearised silent models, but not in the general exact non-linear case. Thus there is a linearisation instability, and it is highly unlikely that there is a large class of silent models. We conjecture that there are no spatially inhomogeneous solutions with Weyl curvature of Petrov type I, and indicate further issues that await clarification.Comment: Minor corrections and improvements; 1 new reference; to appear Class. Quantum Grav.; 16 pages Ioplpp

Maximally extended, explicit and regular coverings of the Schwarzschild - de Sitter vacua in arbitrary dimension

Maximally extended, explicit and regular coverings of the Schwarzschild - de Sitter family of vacua are given, first in spacetime (generalizing a result due to Israel) and then for all dimensions $D$ (assuming a $D-2$ sphere). It is shown that these coordinates offer important advantages over the well known Kruskal - Szekeres procedure.Comment: 12 pages revtex4 5 figures in color. Higher resolution version at http://www.astro.queensu.ca/~lake/regularcoordinates.pd

How to measure spatial distances?

The use of time--like geodesics to measure temporal distances is better justified than the use of space--like geodesics for a measurement of spatial distances. We give examples where a ''spatial distance'' cannot be appropriately determined by the length of a space--like geodesic.Comment: 4 pages, latex, no figure

Collisions of Einstein-Conformal Scalar Waves

A large class of solutions of the Einstein-conformal scalar equations in D=2+1 and D=3+1 is identified. They describe the collisions of asymptotic conformal scalar waves and are generated from Einstein-minimally coupled scalar spacetimes via a (generalized) Bekenstein transformation. Particular emphasis is given to the study of the global properties and the singularity structure of the obtained solutions. It is shown, that in the case of the absence of pure gravitational radiation in the initial data, the formation of the final singularity is not only generic, but is even inevitable.Comment: 17 pages, LaTe

Nonperturbative gravito-magnetic fields

In a cold matter universe, the linearized gravito-magnetic tensor field satisfies a transverse condition (vanishing divergence) when it is purely radiative. We show that in the nonlinear theory, it is no longer possible to maintain the transverse condition, since it leads to a non-terminating chain of integrability conditions. These conditions are highly restrictive, and are likely to hold only in models with special symmetries, such as the known Bianchi and $G_2$ examples. In models with realistic inhomogeneity, the gravito-magnetic field is necessarily non-transverse at second and higher order.Comment: Minor changes to match published version; to appear in Phys. Rev.

Ideally embedded space-times

Due to the growing interest in embeddings of space-time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we extend the notion of ideal embeddings from Riemannian geometry to the indefinite case. Ideal embeddings are such that the embedded manifold receives the least amount of tension from the surrounding space. Then it is shown that the de Sitter spaces, a Robertson-Walker space-time and some anisotropic perfect fluid metrics can be ideally embedded in a five-dimensional pseudo-Euclidean space.Comment: layout changed and typos corrected; uses revtex

Moderate deviations for the determinant of Wigner matrices

We establish a moderate deviations principle (MDP) for the log-determinant $\log | \det (M_n) |$ of a Wigner matrix $M_n$ matching four moments with either the GUE or GOE ensemble. Further we establish Cram\'er--type moderate deviations and Berry-Esseen bounds for the log-determinant for the GUE and GOE ensembles as well as for non-symmetric and non-Hermitian Gaussian random matrices (Ginibre ensembles), respectively.Comment: 20 pages, one missing reference added; Limit Theorems in Probability, Statistics and Number Theory, Springer Proceedings in Mathematics and Statistics, 201

Inter-layer spin diffusion and electric conductivity in the organic conductors {\kappa}-ET2-Cl and {\kappa}-ET2-Br

A high frequency (111.2-420 GHz) electron spin resonance study of the inter-layer (perpendicular) spin diffusion as a function of pressure and temperature is presented in the conducting phases of the layered organic compounds, {\kappa}-(BEDT-TTF)2-Cu[N(CN)2]X ({\kappa}-ET2-X), X=Cl or Br. The resolved ESR lines of adjacent layers at high temperatures and high frequencies allows for the determination of the inter-layer cross spin relaxation time, Tx and the intrinsic spin relaxation time, T2 of single layers. In the bad metal phase spin diffusion is two-dimensional, i.e. spins are not hopping to adjacent layers within T2. Tx is proportional to the perpendicular resistivity at least approximately, as predicted in models where spin and charge excitations are tied together. In {\kappa}-ET2-Cl, at zero pressure Tx increases as the bad metal-insulator transition is approached. On the other hand, Tx decreases as the normal metal and superconducting phases are approached with increasing pressure and/or decreasing temperature.Comment: 18 pages, 11 figure