Effect Of Small-scale Inhomogeneities Research Articles

Einstein clusters as models of inhomogeneous spacetimes

We study the effect of small-scale inhomogeneities for Einstein clusters. We construct a spherically symmetric static spacetime with small-scale radial inhomogeneities and propose the Gedankenexperiment. An hypothetical observer at the center constructs, using limited observational knowledge, a simplified homogeneous model of the configuration. An idealization introduces side effects. The inhomogeneous spacetime and the effective homogeneous spacetime are given by simple solutions to Einstein equations. They provide a basic toy-model for studies of the effect of small-scale inhomogeneities in general relativity. We show that within our highly inhomogeneous model the effect of small-scale inhomogeneities remains small for a central observer. The homogeneous model fits very well to all hypothetical observations as long as their precision is not high enough to reveal a tension.

Inhomogeneity effect in Wainwright-Marshman space-times

Green and Wald have presented a mathematically rigorous framework to study, within general relativity, the effect of small scale inhomogeneities on the global structure of space-time. The framework relies on the existence of a one-parameter family of metrics that approaches the effective background metric in a certain way. Although it is not necessary to know this family in an exact form to predict properties of the backreaction effect, it would be instructive to find explicit examples. In this paper, we provide the first example of such a family of exact non-vacuum solutions to the Einstein's equations. It belongs to the Wainwright-Marshman class and satisfies all of the assumptions of the Green-Wald framework.

New framework for analyzing the effects of small scale inhomogeneities in cosmology

We develop a new, mathematically precise framework for treating the effects of nonlinear phenomena occurring on small scales in general relativity. Our approach is an adaptation of Burnett's formulation of the shortwave approximation, which we generalize to analyze the effects of matter inhomogeneities as well as gravitational radiation. Our framework requires the metric to be close to a background metric, but allows arbitrarily large stress-energy fluctuations on small scales. We prove that, within our framework, if the matter stress-energy tensor satisfies the weak energy condition (i.e., positivity of energy density in all frames), then the only effect that small-scale inhomogeneities can have on the dynamics of the background metric is to provide an effective stress-energy tensor that is traceless and has positive energy density---corresponding to the presence of gravitational radiation. In particular, nonlinear effects produced by small-scale inhomogeneities cannot mimic the effects of dark energy. We also develop perturbation theory off of the background metric. We derive an equation for the long-wavelength part of the leading order deviation of the metric from the background metric, which contains the usual terms occurring in linearized perturbation theory plus additional contributions from the small-scale inhomogeneities. Under various assumptions concerning the absence of gravitational radiation and the nonrelativistic behavior of the matter, we argue that the short-wavelength deviations of the metric from the background metric near a point $x$ should be accurately described by Newtonian gravity, taking into account only the matter lying within a homogeneity length scale of $x$. Finally, we argue that our framework should provide an accurate description of the actual universe.

The effect of small-scale inhomogeneities on ozone depletion in the Arctic

THE chemical processes involved in the depletion of polar stratospheric ozone are now fairly well understood1,2. But the effect of small-scale stirring and mixing of the chemical species involved can be misrepresented in three-dimensional chemical-transport models because of their coarse resolution. Because of the non-linearities in the chemical rate laws, especially those involving chlorine in the main catalytic cycle, these effects can be important—particularly in the Arctic, where the polar vortex is less uniform and less isolated from surrounding air than in the Antarctic. Here we use a very-high-resolution model with simplified ozone-depletion chemistry to show that the depletion is sensitive to small-scale inhomogeneities in the distribution of reactant species. Under the conditions of the winter of 1994–95 the effect is large enough to account for the observed discrepancies of about 40% between modelled and observed ozone depletion in the Arctic environment3–5.

Effect of Small-scale Inhomogeneities on the Dispersive Properties of a Plasma

A theory is developed to describe the effect of small�scale inhomogeneities or 'ripples' in an unmagnetised plasma on the properties of transverse waves with wavelength long compared with the scale length of the ripples. The procedure used is ased on a covariant version of nonlinear plasma kinetic theory. A simpler theory, which is more physically transparent, is explored in an appendix, and is found to reproduce the results of the more rigorous theory only in the simplest limiting cases.