Perfect fluids revisited: an action principle approach

General Relativity and Quantum Cosmology [Submitted on 12 Jun 2026] Title:Perfect fluids revisited: an action principle approach View PDF HTML (experimental)Abstract:We revisit the variational principle for relativistic perfect fluids in a manifestly covariant formulation based on differential forms, with particular attention to the boundary data required for a well-posed action principle. For timelike flows, the formalism is largely a geometric reformulation of the Schutz action principle for perfect fluids. We then analyse the extension of the same variational principle to null flows. In that case, the system is not a generic perfect fluid: the equations of motion force the enthalpy density to vanish, $\rho+P=0$. The resulting stress-energy tensor decomposes into a vacuum energy-like term with variable pressure and a null dust contribution. This shows that the obstruction to the naive fluid extension is dynamical rather than kinematical. Since the matter action is formulated independently of any gravitational field equations, the construction can be generalised to first-order or non-metric theories of gravity. Current browse context: gr-qc References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) IArxiv Recommender (What is IArxiv?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.