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Manuscript IV@1 · IV.tex · figure · 351cb2d7

Fixed vacuum TT plane

Model 1: the fixed vacuum TT plane › A nondegenerate plane and its admitted section · lines 819–854

IV@1#fig:fixed-TT-plane

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(a)Fixed canonical plane
qπer
k=qe+πr,σplane(e,r)=1k=qe+\pi r,\quad \sigma_{\mathrm{plane}}(e,r)=1
(e,e˙)∣t0=(A,0)(e,\dot e)|_{t_0}=(A,0)
(r,r˙)∣t0=(0,A/MA)(r,\dot r)|_{t_0}=(0,A/M_A)
fixed nondegenerate vacuum TT plane
(b)Admitted decomposition
h=k+Kξh=k+K\xi
→
w(h)=ξw(h)=\xi
→
h−Kw(h)=kh-Kw(h)=k
ξ∈Cc∞\xi\in C_c^\infty, D(k)=0D(k)=0, unique on the declared domain
R0i0j(1)(k)=−12k¨ijR^{(1)}_{0i0j}(k)=-\tfrac12\ddot k_{ij}

A pure-gauge plane member would be a harmonic Schwartz field, hence zero.

Model choice, not a gravitational-sector cutoff.

Fixed vacuum TT plane. The normalized waves define one canonical gravitational degree of freedom. On , the retarded harmonic map extracts the compact gauge parameter and returns the unique plane representative. The plane is a model choice, not a gravitational-sector cutoff.

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