Manuscript IX-D-ST@1 · IX-D-ST.tex · definition · b1dc631a

Definition: Chart causal relation

Shared host contract · lines 325–341

IX-D-ST@1#def:chartcausal

For developed points in the laboratory,

(v, z) \in J_{ch}^{-} (t, x) ⟺ v \leq t, ∣ z - x ∣ \leq t - v .

Both null boundaries and coincidence are included. All occurrences of $J^{\pm}$ below mean these chart sets. They are not assertions about all causal curves of the global conical host. For a compact observation set $F$ , put

P_{F} = J_{ch}^{-} (F) \cap {t \geq 0} .

Displayed formulas in this passage

unlabeled · line 328
$(v, z) \in J_{ch}^{-} (t, x) ⟺ v \leq t, ∣ z - x ∣ \leq t - v .$
unlabeled · line 338
$P_{F} = J_{ch}^{-} (F) \cap {t \geq 0} .$

Nearby in this section

section: Shared host contract
proposition: Proposition: The regular product is not globally hyperbolic
section: Shared host contract
section: Shared host contract
assumption: Assumption: Supported carrier input
remark: Remark: What saturation does not say
proposition: Proposition: Description changes do not evolve the host