On the Definition of the Action–Flux Tensor: Physical Content of T^μν(A) in Scalar, Electromagnetic, and Fluid Examples

This paper defines the action–flux tensor T^μν(A) as the symmetric object obtained by metric variation of an action functional J [g; A].
It shows that the familiar stress–energy tensors of scalar, electromagnetic, and relativistic-fluid systems are all special cases of a single conservation-first formulation.

Rather than proposing new physics, the paper reorganizes known results under one unifying principle — the Local Conservation Postulate (LCP),

∂μTμν(A)=0,\partial_\mu T^{\mu\nu}(A)=0,∂μTμν(A)=0,

interpreted as a starting law rather than a derived identity.

The study reproduces all standard tensors exactly and introduces optional small Fold-type corrections as covariant regularisation terms.
For realistic parameters, the corrections are negligible in laboratory and astrophysical regimes, confirming compatibility with general relativity while providing a clear conservation-first structure for future computational and conceptual work.

Related context: https://jpblankert.com/post-einstein-cosmos/
License: CC BY-NC-ND 4.0

Bullet-Point Highlights

• Defines the action–flux tensor T^μν(A) = −(2/√|g|) δJ / δg_μν

• Unifies stress–energy tensors of scalar, electromagnetic, and fluid systems under one conservation-first framework

• States five structural axioms: locality, covariance, symmetry, energy positivity, and conservation consistency

• Confirms that all classical field theories satisfy the same local-balance law ∂_μT^μν=0

• Introduces optional Fold-type regularisation terms α(∇_μJ^μ)² + β J_μJ^μ

• Estimates corrections ≤ 10⁻¹² for realistic systems → consistent with GR

• Suggests measurable tests via high-precision interferometry and ultra-field plasmas

• Clarifies dimensions: [T^μν] = J m⁻³ = N m⁻²

• Reinterprets conservation as the generator of geometry, not its consequence

• Complements the trilogy:

  • Local Conservation and the Tensor Structure of Spacetime (10.5281/zenodo.17450082)

  • From Conservation to Curvature (10.5281/zenodo.17430288)

  • The Landscape of Post-Einstein Cosmologies (10.5281/zenodo.17527108)
    
    Keywords:

    • Local Conservation Postulate (LCP)

    • Action–Flux Tensor

    • Metric-Induced Fold

    • Conservation-First Physics

    • Covariant Energy–Momentum Tensor

    • Stress–Energy in Field Theory

    • Conservation and Geometry

    • Post-Einstein Cosmology

    • Fold-Regular Universe

    • Finite Vacuum Energy

    • Variational Principles

    • Noether and Bianchi Identities

    • Tensor Structure of Spacetime

    • Unified Field Framework

    • Physical Units and Dimensional Analysis

    • Gravitational Consistency Conditions

    • Experimental Falsifiability

    • Femtosecond Interferometry Tests

    • Zenodo Trilogy Continuation