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Manuscript III@2 · III.tex · figure · 82dad3e5

Past-trivial gauges and residual waves

The coupled first-order jet and retarded harmonic section › Past-trivial gauges · lines 1186–1208

III@2#fig:gauge-support-classes

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metricscalarquotient / invariantobstruction / errorsupport / scope
Retarded gauge class
timeJ⁺(K₀)K₀slice before the seed · zero past data
ξ∈E+,□ηξ=0⟹ξ=0\xi\in\mathscr E_+,\quad \Box_\eta\xi=0\Longrightarrow\xi=0
intersection of the two homogeneous-wave classes: zero
C1 residual gauges
t = t₀forwardbackward
□ηξ=0,(ξ,ξ˙)∣t0=(α,β)\Box_\eta\xi=0,\quad (\xi,\dot\xi)|_{t_0}=(\alpha,\beta)
compact, possibly nonzero data · generally not past trivial

The retarded inverse does not select a unique representative modulo all residual waves.

The support requirement is part of the gauge group. The retarded section removes no nonzero C1 residual wave by the identity , because that identity has a different domain.

Nearby in this section