Hybrid Five-Dimensional Gravity with a Constrained Vector

Abstract

We study a one-boundary five-dimensional Einstein–AdS construction coupled to one additional bulk carrier, a Maxwell field whose normalisable zero mode is subject to a unit-timelike constraint and nonlinear interaction on the observer boundary. The reduced boundary theory lies in the generalized Einstein–aether class, but its two-derivative coefficients are restricted by the Maxwell origin: c1 = 1, c3 = −1, c2 = c4 = 0, so c13 = 0 and cT = c at tree level without choosing a point on the generic aether parameter space. The geometric sector yields a normalisable massless graviton, an essential spin–2 continuum threshold at m = 3Hphys/2, and G4 = 2G5/ℓ. In the longitudinal sector we obtain the coupled eikonal positivity condition 0 < (xµ)′ < 1 and vanishing leading weak-field gravitational slip. The local quasi-static limit is an AQUAL equation, but the same stability condition forces a high-acceleration tail whose Solar–Galactic external-field solution is excluded by Cassini/DE440. We therefore analyse a scale-dependent Helmholtz completion restricted explicitly to the longitudinal quasi-static boundary effective theory. Its auxiliary fields add no propagating degree of freedom, it preserves ellipticity, suppresses the Solar quadrupole for ζ ≳ 0.099, and leaves galaxy-scale dynamics essentially unchanged. A fully three-degree-of-freedom covariant completion and its microscopic five-dimensional matching remain open. Conditional compact-object and cosmological applications are kept separate from these gravitational results.