A Space-Time Fluid (Unabridged)

TL;DR

This work reframes general relativity as a space-time fluid by identifying Ricci curvature with fluid properties, yielding a covariant, non-perturbative framework to describe cosmological inhomogeneities and their generation on super-horizon scales via kurvature $K = \frac{8\pi G\rho}{3} - \frac{1}{9}\theta^2$. It draws a precise analogy between classical and space-time fluids, including a local generalized Friedmann structure with local scale factors $a$ and $\bar{a}$ and curvature measures $K$ and $\bar{K}$, and it demonstrates that curvature growth can arise from non-linear hydrodynamic terms such as shear and viscosity, largely independent of gravity. A key practical move is defining a space-time 4-velocity from the center-of-momentum frame, linking spacetime dynamics to matter flow and enabling a tractable evolution equation for kurvature along streamlines. The paper argues that large-scale curvature generation is a non-gravitational process that nonetheless feeds into the observed cosmological inhomogeneities, providing a conceptual and calculational bridge between GR and classical fluid dynamics. This approach has potential implications for understanding the origins of large-scale structure and the role of non-linearities in shaping curvature on cosmological scales.

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.