A Local Metric Action for Gravitational Aether: Construction from Fluid Variational Methods

Version 2.0 substantially revises the earlier extended multiplier formulation. We construct a local classical action consisting of the standard gravitational term, an aether sector and an unchanged ordinary matter action. The matter stress tensor is obtained by varying the ordinary matter action, and the target gravitational-aether equation follows from variation of the physical metric after using the aether field equations.

The construction borrows the first-order pairing structure of Brown (1993), the label-current representation used in fluid effective field theory, and the idea of a comoving clock. It then makes explicit additional choices: p = b pi for the pressure coefficient, a countable internal-field expansion for the remaining scalar coefficient, and a nonregular squared constraint. Within the stated smooth field and variation class, the manuscript gives the full Euler-Lagrange equations and a local lift of every smooth original solution. No fixed equation of state, constant matter trace, irrotational-flow reduction or physical periodic boundary condition is imposed. The paper distinguishes borrowed tools, construction choices and subsequent calculations throughout.

Scope: this establishes a local classical variational correspondence. It does not establish global gluing, equality of physical degrees of freedom, stability or quantization. The Minkowski/FRW degree-of-freedom analysis suggested by the original author remains open. The new countably infinite-field construction has not been verified end to end in Lean. The 19-target/91-theorem verification reported in version 1.1 concerns the earlier, different multiplier extension and must not be interpreted as certification of version 2.0.

This version contains parallel English and Chinese manuscripts and their LaTeX sources, with a scope and change note. Earlier manuscripts and their historical proof packages remain available in the previous versions of this record.

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