Manuscript VI@1 · VI.tex · definition · b5b60afb

Definition: Named solution-jet space

Action, signs, background, and coefficient domain › Formal solution jets · lines 455–474

VI@1#def:jet-space, VI@1#eq:jet-gravity-one, VI@1#eq:jet-gravity-two, VI@1#eq:jet-scalar-zero, VI@1#eq:jet-scalar-one, VI@1#eq:jet-scalar-two

The space $J_{T}$ consists of real smooth tuples $(h, j, ϕ_{0}, ϕ_{1}, ϕ_{2})$ on $M_{T}$ satisfying

G^{(1)} (h) G^{(1)} (j) + G^{(2)} [h, h] P ϕ_{0} P ϕ_{1} P ϕ_{2} = 0, = \frac{1}{4} T (η, ϕ_{0}), = 0, = - L_{h} ϕ_{0}, = - L_{h} ϕ_{1} - (L_{j} + M_{h}) ϕ_{0} .

No assertion that arbitrary unconstrained metric data extend to this space is included in the definition.

Displayed formulas in this passage

VI@1#eq:jet-gravity-one · line 459
$G^{(1)} (h) G^{(1)} (j) + G^{(2)} [h, h] P ϕ_{0} P ϕ_{1} P ϕ_{2} = 0, = \frac{1}{4} T (η, ϕ_{0}), = 0, = - L_{h} ϕ_{0}, = - L_{h} ϕ_{1} - (L_{j} + M_{h}) ϕ_{0} .$
VI@1#eq:jet-gravity-two · line 459
$G^{(1)} (h) G^{(1)} (j) + G^{(2)} [h, h] P ϕ_{0} P ϕ_{1} P ϕ_{2} = 0, = \frac{1}{4} T (η, ϕ_{0}), = 0, = - L_{h} ϕ_{0}, = - L_{h} ϕ_{1} - (L_{j} + M_{h}) ϕ_{0} .$
VI@1#eq:jet-scalar-zero · line 459
$G^{(1)} (h) G^{(1)} (j) + G^{(2)} [h, h] P ϕ_{0} P ϕ_{1} P ϕ_{2} = 0, = \frac{1}{4} T (η, ϕ_{0}), = 0, = - L_{h} ϕ_{0}, = - L_{h} ϕ_{1} - (L_{j} + M_{h}) ϕ_{0} .$
VI@1#eq:jet-scalar-one · line 459
$G^{(1)} (h) G^{(1)} (j) + G^{(2)} [h, h] P ϕ_{0} P ϕ_{1} P ϕ_{2} = 0, = \frac{1}{4} T (η, ϕ_{0}), = 0, = - L_{h} ϕ_{0}, = - L_{h} ϕ_{1} - (L_{j} + M_{h}) ϕ_{0} .$
VI@1#eq:jet-scalar-two · line 459
$G^{(1)} (h) G^{(1)} (j) + G^{(2)} [h, h] P ϕ_{0} P ϕ_{1} P ϕ_{2} = 0, = \frac{1}{4} T (η, ϕ_{0}), = 0, = - L_{h} ϕ_{0}, = - L_{h} ϕ_{1} - (L_{j} + M_{h}) ϕ_{0} .$