Manuscript III-B@1 · III-B-v1.tex · section · d2c98f62

The equation space and its action

The retained first-order jet and its retarded section › The equation space and its action · lines 948–971

III-B@1#eq:jet-action

Let $J_{R}$ consist of triples

(h, ϕ_{0}, ϕ_{1})

such that

h \in M_{R}, G^{(1)} (h) = 0, P ϕ_{0} = 0, P ϕ_{1} = - L_{h} ϕ_{0},

with the scalar Cauchy data supported in $B_{r_{*}}$ . The forced equation and Lemma lem:evolution keep the scalars in $C_{r_{*}}$ .

For field-independent $ξ \in G_{R}$ , set

T_{ξ} (h, ϕ_{0}, ϕ_{1}) = (h + K ξ, ϕ_{0}, ϕ_{1} + X_{ξ} ϕ_{0}) .

Displayed formulas in this passage

III-B@1#eq:jet-action · line 966
$T_{ξ} (h, ϕ_{0}, ϕ_{1}) = (h + K ξ, ϕ_{0}, ϕ_{1} + X_{ξ} ϕ_{0}) .$
unlabeled · line 951
$(h, ϕ_{0}, ϕ_{1})$
unlabeled · line 955
$h \in M_{R}, G^{(1)} (h) = 0, P ϕ_{0} = 0, P ϕ_{1} = - L_{h} ϕ_{0},$