Thermal boundaries for relativistic fluids without a conserved charge
Abstract
We study an ultrarelativistic fluid with no conserved particle number in a planar slab geometry bounded by two parallel, thermally conducting plates held at fixed (possibly different) temperatures. The fluid-wall interaction is described within kinetic theory by modeling the fluid as self-interacting radiation: a gas of bosons emitted and absorbed by the walls according to black-body laws, while mutual collisions enforce local equilibration. From this microscopic setup we derive effective boundary conditions for the hydrodynamic fields, finding that the walls behave as modified absorbing boundaries (and not as thermostats). In particular, the fluid temperature at the boundary does not generally coincide with the wall temperature. We prove that the resulting initial-boundary-value problem is well posed. When the plates are held at different temperatures, the system develops a uniform steady flow from the hotter to the colder wall, with energy density equal to the arithmetic mean of the corresponding black-body energy densities in the limit of a small temperature difference.
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BibTeX
@misc{gavassino2026thermal,
title = {{Thermal boundaries for relativistic fluids without a conserved charge}},
author = {Lorenzo Gavassino and Soeren Schlichting and Gabriel S. Denicol},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04925},
eprint = {2609.04925},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04925},
}
RIS
TY - UNPB
TI - Thermal boundaries for relativistic fluids without a conserved charge
AU - Lorenzo Gavassino
AU - Soeren Schlichting
AU - Gabriel S. Denicol
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04925
UR - https://arxiv.org/abs/2609.04925
AB - We study an ultrarelativistic fluid with no conserved particle number in a planar slab geometry bounded by two parallel, thermally conducting plates held at fixed (possibly different) temperatures. The fluid-wall interaction is described within kinetic theory by modeling the fluid as self-interacting radiation: a gas of bosons emitted and absorbed by the walls according to black-body laws, while mutual collisions enforce local equilibration. From this microscopic setup we derive effective boundary conditions for the hydrodynamic fields, finding that the walls behave as modified absorbing boundaries (and not as thermostats). In particular, the fluid temperature at the boundary does not generally coincide with the wall temperature. We prove that the resulting initial-boundary-value problem is well posed. When the plates are held at different temperatures, the system develops a uniform steady flow from the hotter to the colder wall, with energy density equal to the arithmetic mean of the corresponding black-body energy densities in the limit of a small temperature difference.
ER -