Manuscript XI-C@1 · XI-C.tex · section · acec1422

Causal support and the limits of the diagnostics

Causal support and the limits of the diagnostics · lines 919–946

The closed support of the smooth ramp can meet $t = 0$ . It is not a claim that $σ_{ε}$ is nonzero there. Nor is (eq:zsupport) a ramp-layer support statement: the tree can propagate and remain nonzero long after $ε$ .

A pure-gauge diagnostic must be stated correctly:

G_{lin} [K ξ] = 0, D (K ξ) = □ ξ .

For compact plateau $ξ$ , the second expression is not generally zero. In fact

(- □ P) (K ξ) = - P K (□ ξ) .

Thus invisibility to the invariant linearized Einstein tensor does not imply invisibility to the gauge-fixed operator.

Moreover, the tree (eq:T) has no external metric argument to set equal to $K ξ$ . Its source is the scalar stress. A claimed vanishing of this tree merely because an unrelated classical background is pure gauge is therefore not a diagnostic of the constructed contraction.

Displayed formulas in this passage

unlabeled · line 928
$G_{lin} [K ξ] = 0, D (K ξ) = □ ξ .$
unlabeled · line 933
$(- □ P) (K ξ) = - P K (□ ξ) .$

Nearby in this section

proposition: Proposition: Intermediate and external support