Field equation analysis near infinity in massive Hellings-Nordtvedt theory restricts the model to two single-coupling sectors; the A²R sector yields asymptotically flat Schwarzschild black holes with radial vector fields and neutron stars with measurable deviations from GR while satisfying weak-fiel
On the 4D generalized Proca action for an Abelian vector field
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abstract
We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated St\"uckelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the St\"uckelberg field describing the longitudinal mode, which is in agreement with the results of JCAP 1405, 015 (2014) and Phys. Lett. B 757, 405 (2016) and complements those of JCAP 1602, 004 (2016). We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field $A_\mu$, the Faraday tensor $F_{\mu \nu}$ and its Hodge dual $\tilde{F}_{\mu \nu}$.
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gr-qc 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Black holes and neutron stars in massive Hellings-Nordtvedt theory
Field equation analysis near infinity in massive Hellings-Nordtvedt theory restricts the model to two single-coupling sectors; the A²R sector yields asymptotically flat Schwarzschild black holes with radial vector fields and neutron stars with measurable deviations from GR while satisfying weak-fiel