Stable evolution of relativistic hydrodynamics order-by-order in gradients
Stable evolution of relativistic hydrodynamics order-by-order in gradients
We provide a systematic framework for solving the initial value problem for relativistic hydrodynamics formulated as a gradient expansion. Secular growth is handled by a suitable covariant resummation scheme, which reorganises the degrees of freedom at each order in the expansion while preserving the sum. Our scheme can be applied to any order in the gradient expansion; we provide the explicit formulation at first and second orders. When working to first order, we find that the BDNK equations of motion emerge as an intermediate step in a calculation performed in the Landau frame. We show that non-hydrodynamic modes appear only in such intermediate calculations and cancel when evaluating solutions to the required order. Our procedure does not introduce any other fields or require any additional initial data beyond those appearing in the theory of ideal fluids.
Heller, Michal P.
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Serantes, Alexandre
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Spaliński, Michał
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Withers, Benjamin
e510375b-c5d2-4d5f-bd68-40ace13f0ec9
11 November 2025
Heller, Michal P.
5b6c6d3e-4731-414d-8556-bd8604ce5377
Serantes, Alexandre
e19687f5-de76-4cb3-9afa-c9d843c3f5e2
Spaliński, Michał
3fabf22d-7873-492c-8bc6-6101c914c2b0
Withers, Benjamin
e510375b-c5d2-4d5f-bd68-40ace13f0ec9
Heller, Michal P., Serantes, Alexandre, Spaliński, Michał and Withers, Benjamin
(2025)
Stable evolution of relativistic hydrodynamics order-by-order in gradients.
arXiv.
(doi:10.48550/arXiv.2511.08582).
Abstract
We provide a systematic framework for solving the initial value problem for relativistic hydrodynamics formulated as a gradient expansion. Secular growth is handled by a suitable covariant resummation scheme, which reorganises the degrees of freedom at each order in the expansion while preserving the sum. Our scheme can be applied to any order in the gradient expansion; we provide the explicit formulation at first and second orders. When working to first order, we find that the BDNK equations of motion emerge as an intermediate step in a calculation performed in the Landau frame. We show that non-hydrodynamic modes appear only in such intermediate calculations and cancel when evaluating solutions to the required order. Our procedure does not introduce any other fields or require any additional initial data beyond those appearing in the theory of ideal fluids.
Text
2511.08582v1
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Published date: 11 November 2025
Identifiers
Local EPrints ID: 507669
URI: http://eprints.soton.ac.uk/id/eprint/507669
ISSN: 2331-8422
PURE UUID: c5103e07-eae6-405c-90d2-de54f71361e6
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Date deposited: 16 Dec 2025 18:28
Last modified: 17 Dec 2025 02:27
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Contributors
Author:
Michal P. Heller
Author:
Alexandre Serantes
Author:
Michał Spaliński
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