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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.21359 |
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| _version_ | 1866910241323483136 |
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| author | Wang, Zhi-Wei Braunstein, Samuel L. |
| author_facet | Wang, Zhi-Wei Braunstein, Samuel L. |
| contents | All standard formulations of relativistic dissipative hydrodynamics, from Eckart through Israel-Stewart to the recent BDNK framework, assume that the viscous stress depends on the shear tensor $σ_{αβ}$ and the expansion scalar $θ$ but not on the vorticity $ω_{αβ}$ or the acceleration $a_α$. We derive this structure from a Lagrangian kinematic construction on Lorentzian spacetimes, extending a recent result on Riemannian manifolds. The spatial strain rate, constructed from the rate of change of spatial inner products of Lie-dragged connecting vectors, is the spatially projected Lie derivative of the projected metric $h_{αβ} = g_{αβ} + u_αu_β$. The acceleration terms drop out exactly under spatial projection, and the vorticity cancels by symmetry. We show that material frame-indifference fails for generic Killing perturbations by an amount $δ\mathfrak{h}_{αβ} = +ε(ξ_αa_β+ ξ_βa_α)$ proportional to the acceleration, and is restored only for flow-preserving isometries. We prove that the non-relativistic limit of the BDNK equations gives the deformation Laplacian universally in the viscous sector, with the BDNK parameter dependence identified by Hegade K R, Ripley, and Yunes arising entirely from the thermal (heat-flux) sector. As an application, we derive the Weinberg gravitational-wave damping formula directly from the kinematic strain rate in a perturbed FRW spacetime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21359 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Kinematic selection of the viscous stress in relativistic dissipative hydrodynamics Wang, Zhi-Wei Braunstein, Samuel L. General Relativity and Quantum Cosmology All standard formulations of relativistic dissipative hydrodynamics, from Eckart through Israel-Stewart to the recent BDNK framework, assume that the viscous stress depends on the shear tensor $σ_{αβ}$ and the expansion scalar $θ$ but not on the vorticity $ω_{αβ}$ or the acceleration $a_α$. We derive this structure from a Lagrangian kinematic construction on Lorentzian spacetimes, extending a recent result on Riemannian manifolds. The spatial strain rate, constructed from the rate of change of spatial inner products of Lie-dragged connecting vectors, is the spatially projected Lie derivative of the projected metric $h_{αβ} = g_{αβ} + u_αu_β$. The acceleration terms drop out exactly under spatial projection, and the vorticity cancels by symmetry. We show that material frame-indifference fails for generic Killing perturbations by an amount $δ\mathfrak{h}_{αβ} = +ε(ξ_αa_β+ ξ_βa_α)$ proportional to the acceleration, and is restored only for flow-preserving isometries. We prove that the non-relativistic limit of the BDNK equations gives the deformation Laplacian universally in the viscous sector, with the BDNK parameter dependence identified by Hegade K R, Ripley, and Yunes arising entirely from the thermal (heat-flux) sector. As an application, we derive the Weinberg gravitational-wave damping formula directly from the kinematic strain rate in a perturbed FRW spacetime. |
| title | Kinematic selection of the viscous stress in relativistic dissipative hydrodynamics |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2605.21359 |