Nonlinear perturbations for dissipative and interacting relativistic fluids

TL;DR

This work develops a covariant, fully nonlinear perturbation formalism for dissipative and interacting relativistic fluids by leveraging the covector $\zeta_a = D_a \alpha - \frac{\dot{\alpha}}{\dot{\rho}} D_a \rho$, a nonlinear generalization of the curvature perturbation. It derives a general identity for nonlinear covectors and constructs evolution equations for covectors associated with particle number, energy density, and entropy, including dissipative sources. The authors extend the framework to multifluid systems with energy-momentum transfer, decomposing perturbations into intrinsic and relative nonadiabatic components and showing that the nonlinear equations mimic linear theory while remaining covariant. The results reduce to the known perfect-fluid and linear perturbation equations in appropriate limits, and the formalism provides a coordinate-free tool for higher-order analyses with potential cosmological applications. Overall, the paper delivers a robust nonlinear, covariant toolkit for analyzing dissipative and interacting relativistic fluids in curved spacetimes.

Abstract

We develop a covariant formalism to study nonlinear perturbations of dissipative and interacting relativistic fluids. We derive nonlinear evolution equations for various covectors defined as linear combinations of the spatial gradients of the local number of e-folds and of some scalar quantities characterizing the fluid, such as the energy density or the particle number density. For interacting fluids we decompose perturbations into adiabatic and entropy components and derive their coupled evolution equations, recovering and extending the results obtained in the context of the linear theory. For non-dissipative and noninteracting fluids, these evolution equations reduce to the conservation equations that we have obtained in recent works. We also illustrate geometrically the meaning of the covectors that we have introduced.

Figures (1)

• Figure 1: Geometric interpretation of $\zeta_a$.