A Space-Time Fluid (Unabridged)

TL;DR

This paper reformulates general relativity as a fluid dynamics problem, providing a covariant, non-perturbative framework to describe cosmological inhomogeneities and their evolution, especially on super-horizon scales.

Contribution

It introduces a space-time fluid analogy for general relativity, offering a simple, covariant, and non-perturbative method to analyze cosmological inhomogeneities and their dynamics.

Findings

Kurvature measures cosmological inhomogeneities covariantly.

Space-time fluid dynamics closely resemble classical fluid behavior.

Kurvature increases due to non-linear effects, not just gravity.

Abstract

Purpose: This essay is a retelling of general relativity in a language in which space-time geometry is expressed as a fluid. This trivial and useful reformulation gives 1) a non-perturbative covariant description of cosmological inhomogeneities and 2) a simple formula describing how cosmic inhomogeneities are generated on super-horizon scales. Methods: Equating the Ricci curvature with the associated matter stress-energy gives a description of space-time geometry in terms of fluid properties. These locally measurable (covariant) non-perturbative quantities are in some ways superior to commonly used "gauge invariant" quantities. The dynamics of a quantity (kurvature) which describes cosmological inhomogeneities is described in detail. A detailed comparison is made of space-time fluid dynamics with that of a classical (Newtonian physics) fluid. Results: The fluid lexicon permits an unambiguous definition of the velocity of space-time. The evolution of the space-time fluid is in many ways identical with that of the classical fluid when expressed in Lagrangian coordinates. Kurvature is a measure of the specific binding energy of the fluid and is a most useful covariant measure of cosmological inhomogeneities. For plausible matter models kurvature will increase, even on super-horizon scales, due to non-linear hydrodynamic effects rather than gravity. This phenomena is also exhibited by classical fluids. Conclusion: The space-time fluid representation of geometrodynamics gives a simple and useful description of the evolution of cosmological inhomogeneities.