Manuscript X-A-ST@1 · X-A-ST.tex · definition · d9ccbde1

Definition: Supported regular chart

The prescribed host and the flat-completion ledger · lines 274–305

X-A-ST@1#def:chart, X-A-ST@1#eq:retainedshadow

Choose an injective product developing chart

ι : L ⟶ M^{\circ}, L = (- a, T_{*} + a) \times B_{R} (x_{*}), a > 0,

whose relevant compact closure stays off $W$ . Set $t = c (T - T_{Σ})$ on its image. In developed coordinates,

ι^{*} G = - d t^{2} + d x^{2} .

Choose a relatively compact open observation region $O ⋐ (0, T_{*}) \times B_{R} (x_{*})$ such that

D_{*} := J_{η}^{-} (O) \cap ([0, T_{*}] \times R^{3}) ⋐ L .

Only tests $f \in C_{c}^{\infty} (O; R)$ are used for the supported observable.

All nested retarded calculations for such a test are retained in $D_{*}$ . No independently adjustable lateral boundary datum is introduced.

Displayed formulas in this passage

unlabeled · line 277
$ι : L ⟶ M^{\circ}, L = (- a, T_{*} + a) \times B_{R} (x_{*}), a > 0,$
unlabeled · line 286
$ι^{*} G = - d t^{2} + d x^{2} .$
X-A-ST@1#eq:retainedshadow · line 293
$D_{*} := J_{η}^{-} (O) \cap ([0, T_{*}] \times R^{3}) ⋐ L .$