Manuscript VII-A@1 · VII-A.tex · definition · 11da3fe6

Definition: Plateau Einstein–scalar coupling jet

Restriction to a named Einstein–scalar coupling jet › Coupling expansion versus a scalar background · lines 1437–1458

VII-A@1#def:jet, VII-A@1#eq:Ein1, VII-A@1#eq:Ein2

The space $J_{2}^{g}$ consists of tuples

(h, k, ϕ_{0}, ϕ_{1, g}, ϕ_{2, g})

such that:

$P_{m} ϕ_{0} = 0$ ;
the scalar coefficients are the zero-data solutions (eq:phi1)–(eq:phi2);
the metric coefficients satisfy
$G^{(1)} [h] G^{(1)} [k] + G^{(2)} [h, h] = 0, = T^{(0)} [ϕ_{0}] .$

No zero-Cauchy-data condition is imposed on $h$ or $k$ .

Displayed formulas in this passage

VII-A@1#eq:Ein1 · line 1449
$G^{(1)} [h] G^{(1)} [k] + G^{(2)} [h, h] = 0, = T^{(0)} [ϕ_{0}] .$
VII-A@1#eq:Ein2 · line 1449
$G^{(1)} [h] G^{(1)} [k] + G^{(2)} [h, h] = 0, = T^{(0)} [ϕ_{0}] .$
unlabeled · line 1440
$(h, k, ϕ_{0}, ϕ_{1, g}, ϕ_{2, g})$