Manuscript XVI-D@1 · XVI-D.tex · section · b73c6f4a

Explicit witness response and traceless channel

Explicit witness response and traceless channel · lines 802–818

XVI-D@1#eq:Vlambda, XVI-D@1#eq:Rlambda

Define the ambient particular field

V_{λ}^{μν} (t) = \int_{0}^{t} (t - s) S_{λ}^{μν} (s) d s,

and set

R_{λ} = - P V_{λ} .

For negative $t$ the integral is zero, because its source is zero there. This is a smooth past-zero extension, not a sharp multiplication of a nonvanishing solution.

Displayed formulas in this passage

XVI-D@1#eq:Vlambda · line 805
$V_{λ}^{μν} (t) = \int_{0}^{t} (t - s) S_{λ}^{μν} (s) d s,$
XVI-D@1#eq:Rlambda · line 811
$R_{λ} = - P V_{λ} .$

Nearby in this section

lemma: Lemma: Explicit zero-data solution
proposition: Proposition: Witness response identification
section: Explicit witness response and traceless channel