Manuscript IX-D@3 · IX-D-v3.tex · section · 3ad4586e

Actual functional support

D1: domains and separate causal interfaces › Actual functional support · lines 761–782

IX-D@3#eq:ordering

Observation support and functional support are not interchangeable. The metric dependence of $B_{f}$ generally extends from $supp f$ back to the initial surface.

We use $J^{\pm}$ for causal future and past, including null relations, and $I^{\pm}$ for chronological future and past. A binary ordering condition is

F ≳ G ⟺ supp_{fun} F \cap J^{-} (supp_{fun} G) = \emptyset .

Equivalently,

supp_{fun} G \cap J^{+} (supp_{fun} F) = \emptyset .

This means that $F$ is not causally earlier than $G$ ; it also includes spacelike-separated supports.

Displayed formulas in this passage

IX-D@3#eq:ordering · line 770
$F ≳ G ⟺ supp_{fun} F \cap J^{-} (supp_{fun} G) = \emptyset .$
unlabeled · line 777
$supp_{fun} G \cap J^{+} (supp_{fun} F) = \emptyset .$

Nearby in this section

definition: Definition: Configuration support