# Multifluid Modelling of Relativistic Radiation Hydrodynamics

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Multifluid Hydrodynamics

#### 2.1. Non-Dissipative Evolution of Relativistic Multifluids

#### 2.2. Including Dissipation

## 3. Heat Conduction and Bulk Viscosity

#### 3.1. Heat Conduction

#### 3.2. Bulk Viscosity

## 4. Radiation Hydrodynamics

#### 4.1. The Hydrodynamic Model

#### 4.2. The Dissipative Terms

#### 4.3. Thermodynamic Analysis of the Dissipative Terms

#### 4.4. Application: Deriving the Four-Force ${G}_{\nu}$ from Thermodynamic Arguments

- i
- the thermal coefficients obey the Kirchhoff law,
- ii
- the scattering is isotropic and coherent,
- iii
- the opacities have a grey-body form.

- i
- every dissipative process contributes additively to the transport coefficients and the thermodynamic constraints presented in the previous subsection hold separately for every microscopic contribution,
- ii
- the degeneracy assumption we presented in Section 4.2, which allows reducing the degrees of freedom of the model from 10 to 9, is fulfilled also by ${G}_{\nu}$.

#### 4.5. Deriving the Reaction Rate From Thermodynamic Arguments

## 5. Radiation as a Source of Bulk Viscosity

## 6. Radiation Hydrodynamics as a Model for Heat Conduction

#### 6.1. The Origin of the Entrainment

#### 6.2. Energy-Momentum Tensor

#### 6.3. The Hydrodynamic Equations

#### 6.4. Heat Conductivity Coefficient

## 7. Limitations of the Model

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Triangular vs. Square Formulation

## Appendix B. The Relaxation-Time Approximation

## Appendix C. Calculations

#### Appendix C.1. Onsager Symmetry of the Dissipative Coefficients

#### Appendix C.2. Computation of the Bulk Viscosity Coefficient

#### Appendix C.3. Eckart Decomposition of the Entropy Current

## Appendix D. Radiation-Mediated Bulk Viscosity of Non-Degenerate Ideal Gases

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Gavassino, L.; Antonelli, M.; Haskell, B.
Multifluid Modelling of Relativistic Radiation Hydrodynamics. *Symmetry* **2020**, *12*, 1543.
https://doi.org/10.3390/sym12091543

**AMA Style**

Gavassino L, Antonelli M, Haskell B.
Multifluid Modelling of Relativistic Radiation Hydrodynamics. *Symmetry*. 2020; 12(9):1543.
https://doi.org/10.3390/sym12091543

**Chicago/Turabian Style**

Gavassino, Lorenzo, Marco Antonelli, and Brynmor Haskell.
2020. "Multifluid Modelling of Relativistic Radiation Hydrodynamics" *Symmetry* 12, no. 9: 1543.
https://doi.org/10.3390/sym12091543