The general relativistic equations of radiation hydrodynamics in the viscous limit

Eric R. Coughlin, Mitchell C. Begelman

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energy-momentum tensor in the diffusion limit with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the four-velocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and do not depend on thermodynamic arguments such as the assignment of a temperature to the zeroth-order photon distribution. We perform a perturbation analysis on our equations and demonstrate that as long as the wave numbers do not probe scales smaller than the mean free path of the radiation, the viscosity contributes only decaying, i.e., stable, corrections to the dispersion relations. The astrophysical applications of our equations, including jets launched from super-Eddington tidal disruption events and those from collapsars, are discussed and will be considered further in future papers.

Original languageEnglish (US)
Article number103
JournalAstrophysical Journal
Issue number2
StatePublished - Dec 20 2014
Externally publishedYes


  • Radiation: Dynamics
  • Radiative transfer
  • Relativistic processes

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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