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<p>We compute the linearised dispersion relations of shear waves, heat waves, and sound waves in relativistic “matter+radiation” fluids with grey absorption opacities. This is done by solving radiation hydrodynamics perturbatively in the ratio “radiation stress-energy”/“matter stress-energy”. The resulting expressions <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10509_2025_4395_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="64" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>ω</mi> <mspace width="0.2em" /> <mo>=</mo> <mspace width="0.2em" /> <mi>ω</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$\omega \, {=} \, \omega (k)$</EquationSource> </InlineEquation> accurately describe the hydrodynamic evolution for any <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10509_2025_4395_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>k</mi> <mspace width="0.2em" /> <mo>∈</mo> <mspace width="0.2em" /> <mi mathvariant="double-struck">R</mi> </math></EquationSource> <EquationSource Format="TEX">$k\, {\in }\, \mathbb{R}$</EquationSource> </InlineEquation>. General features of the dynamics (e.g., covariant stability, propagation speeds, and damping of discontinuities) are argued directly from the analytic form of these dispersion relations.</p>

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Dispersion relations of relativistic radiation hydrodynamics

  • 期刊论文

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  • 发表日期：

    2025年1月15日

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  • Lorenzo Gavassino

摘要

We compute the linearised dispersion relations of shear waves, heat waves, and sound waves in relativistic “matter+radiation” fluids with grey absorption opacities. This is done by solving radiation hydrodynamics perturbatively in the ratio “radiation stress-energy”/“matter stress-energy”. The resulting expressions ω = ω ( k ) $\omega \, {=} \, \omega (k)$ accurately describe the hydrodynamic evolution for any k ∈ R $k\, {\in }\, \mathbb{R}$ . General features of the dynamics (e.g., covariant stability, propagation speeds, and damping of discontinuities) are argued directly from the analytic form of these dispersion relations.