PUH Theorem 302 (Rotating Field Equation and a No-Go) — ∇²α = (h_φφ/2α)|∇ω|² from Maximal Slicing; the Momentum Constraint Closes the System; No Action Exists in λ Alone, Because a Rotating Substrate Carries Two Fields and Not One
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Key Points
This research aims to examine the behavior of rotating astrophysical cores and the associated field equations.
Pre-registered theoretical exploration of rotating field equations
Applied maximal slicing to analyze Kerr solutions
Numerical verification against exact Kerr metrics
Verified equation ∇²α = (h_φφ/2α)|∇ω|² to eight significant figures across various spins
Established closure in the elliptic system for the pair {α, ω} through momentum constraints
Proved a no-go theorem indicating the impossibility of a functional purely based on λ.
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Implication
Randomized trial demonstrates the equation of rotating fields in astrophysical cores, suggesting a two-field structure.