Interaction of fluids described through relative motion and application to Bianchi type-I spacetimes
Abstract
We study a model of two fluids with an interaction that depends on their relative motion. The interaction is described using the particle number density of each fluid measured in the rest frame of the other, providing a geometric interpretation of a class of interactions studied in relativistic multifluid theory. We derive the corresponding stress-energy tensor and show that its structure agrees with established results. In particular, the interaction introduces a dependence on the scalar product of the $4$-velocities, which can be expressed in terms of the relative speed of the fluid elements. Furthermore, the relative motion produces unequal pressures along and perpendicular to the direction of motion, together with an energy flux. As an application, we consider a Bianchi type-I universe dominated by one fluid, with the second fluid acting as a source of small anisotropy. We examine how the interaction influences the relative speed and the evolution of cosmological anisotropy. We identify conditions under which the anisotropy decays in the late-time limit, generalizing results for non-interacting fluids from the literature.
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BibTeX
@misc{meszaros2026interaction,
title = {{Interaction of fluids described through relative motion and application to Bianchi type-I spacetimes}},
author = {Peter Mészáros and Daniel Račko},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.16268},
eprint = {2606.16268},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.16268},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Interaction of fluids described through relative motion and application to Bianchi type-I spacetimes
AU - Peter Mészáros
AU - Daniel Račko
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2606.16268
UR - https://arxiv.org/abs/2606.16268
AB - We study a model of two fluids with an interaction that depends on their relative motion. The interaction is described using the particle number density of each fluid measured in the rest frame of the other, providing a geometric interpretation of a class of interactions studied in relativistic multifluid theory. We derive the corresponding stress-energy tensor and show that its structure agrees with established results. In particular, the interaction introduces a dependence on the scalar product of the $4$-velocities, which can be expressed in terms of the relative speed of the fluid elements. Furthermore, the relative motion produces unequal pressures along and perpendicular to the direction of motion, together with an energy flux. As an application, we consider a Bianchi type-I universe dominated by one fluid, with the second fluid acting as a source of small anisotropy. We examine how the interaction influences the relative speed and the evolution of cosmological anisotropy. We identify conditions under which the anisotropy decays in the late-time limit, generalizing results for non-interacting fluids from the literature.
ER -