Equations of General Relativistic Radiation Hydrodynamics from Tensor Formalism

Abstract

Radiation interacts with matter via exchange of energy and momentum. When matter is moving with a relativistic velocity or when the background spacetime is strongly curved, rigorous relativistic treatment of hydrodynamics and radiative transfer is required. Here, we derive fully general relativistic radiation hydrodynamic equations from a covariant tensor formalism. The equations can be applied to any three-dimensional problems and are rather starightforward to understand compared to the comoving frame-based equations. Current approach is applicable to any spacetime or coordinates, but in this work we specifically choose the Schwarzschild spacetime to show explicitly how the hydrodynamic and the radiation moment equations are derived. Some important aspects of relativistic radiation hydrodynamics and the difficulty with the radiation moment formalism are discussed as well.

arXiv comment7 pages, no figure. Section on Closure Relation revised. MNRAS accepted

References in corpus (4)

• A Finite Difference Representation of Neutrino Radiation Hydrodynamics in Spherically Symmetric General Relativistic Space-Time
• General relativistic radiative transfer in hot astrophysical plasmas: a characteristic approach
• Radiatively driven rotating pair-plasma jets from two component accretion flows
• Dynamically Comptonized Spectra from Near Critical Accretion onto Neutron Stars

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