Manuscript Oai365-A@1 · Oai365-A.tex · proposition · a3840e3d

Proposition: Static data do not determine the lapse

Riemannian recovery does not select Lorentzian causality · lines 1088–1107 · proof included or linked

Oai365-A@1#prop:lapse

Even exact knowledge of a spatial pair $(g, A)$ and its DN form does not choose among

G_{N} = - N (x)^{2} d T^{2} + g, N (x) > 0.

At a fixed spatial point, these comparators have different coordinate null slopes when their lapse values differ.

Proof. The spatial operator $\nabla_{A}^{*} \nabla_{A}$ and (eq:DNform) do not contain $N$ . The null equation is

N (x)^{2} d T^{2} = g_{x} (d x, d x),

which depends on $N$ .

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