Manuscript Em06-B@1 · Em06-B-v1.tex · section · 61e38859

Coordinate prescription and observable

Frozen conventions and the classical object › Coordinate prescription and observable · lines 291–309

Em06-B@1#eq:w

For $t \geq 0$ , define the unswitched coordinate coefficient by

□ w [h]^{μ} = C (h)^{μ}, w [h]^{μ} ∣_{Σ_{0}} = 0, \partial_{t} w [h]^{μ} ∣_{Σ_{0}} = 0.

These are coordinate-time Cauchy data. They are not replaced by a metric-dependent normal-derivative prescription.

For a real smooth solution $P_{m} ϕ_{0} = 0$ , define

ϕ_{1, χ} [h; ϕ_{0}] = - G_{m}^{R} Q_{χ h} ϕ_{0} .

The source is compact and separated from $Σ_{0}$ , and the response has zero initial data.

Displayed formulas in this passage

Em06-B@1#eq:w · line 294
$□ w [h]^{μ} = C (h)^{μ}, w [h]^{μ} ∣_{Σ_{0}} = 0, \partial_{t} w [h]^{μ} ∣_{Σ_{0}} = 0.$
unlabeled · line 304
$ϕ_{1, χ} [h; ϕ_{0}] = - G_{m}^{R} Q_{χ h} ϕ_{0} .$