Covariant linear response theory for a photon gas in curved spacetime
Abstract
To overcome the failure of the conventional non-relativistic description of statistics in strong gravitational fields, we develop a covariant theory for a photon gas in curved spacetime, starting from the Boltzmann equation and employing the relaxation time approximation. The transport coefficients are computed up to second order, which are not a massless limit of the massive-particle results due to the fundamentally different phase-space geometry of null particles. At second order, the gravitational field renders the coefficients tensor-valued and induces transverse fluxes, analogous to the Hall effect. Using the first-order results, we derive relativistic generalizations of Fick's and Fourier's laws and obtain the radiation diffusion equation for spherically symmetric accretion disks. This provides a covariant description of radiative transport in strong gravitational fields for high-energy astrophysical applications.
Related
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BibTeX
@misc{wang2026covariant,
title = {{Covariant linear response theory for a photon gas in curved spacetime}},
author = {Jianan Wang and Long Cui and Bin Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02615},
eprint = {2609.02615},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02615},
}
RIS
TY - UNPB
TI - Covariant linear response theory for a photon gas in curved spacetime
AU - Jianan Wang
AU - Long Cui
AU - Bin Wu
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02615
UR - https://arxiv.org/abs/2609.02615
AB - To overcome the failure of the conventional non-relativistic description of statistics in strong gravitational fields, we develop a covariant theory for a photon gas in curved spacetime, starting from the Boltzmann equation and employing the relaxation time approximation. The transport coefficients are computed up to second order, which are not a massless limit of the massive-particle results due to the fundamentally different phase-space geometry of null particles. At second order, the gravitational field renders the coefficients tensor-valued and induces transverse fluxes, analogous to the Hall effect. Using the first-order results, we derive relativistic generalizations of Fick's and Fourier's laws and obtain the radiation diffusion equation for spherically symmetric accretion disks. This provides a covariant description of radiative transport in strong gravitational fields for high-energy astrophysical applications.
ER -