Manuscript XX-E@1 · XX-E.tex · section · cf7a8f40

An identical-prescription escaping-source example

Refinement non-determination and why removal is not entered › An identical-prescription escaping-source example · lines 1367–1393

XX-E@1#eq:escaping

The following example is entirely classical and uses the same original spatial inverse.

Choose a nonnegative, nonzero $ρ \in C_{c}^{\infty} ((1, 2))$ and define

η (Y) = Y_{1} ρ (∣ Y ∣) .

Choose $τ \in C_{c}^{\infty} (I)$ . For $R \geq 1$ , take the metric input

h_{ij, R} (t, y) = 2 a (t)^{2} τ (t) R^{- 1} η (y / R) δ_{ij}, h_{00, R} = h_{0 i, R} = φ_{R} = 0.

Then

(\calCz_{R})^{ia} = τ (t) R^{- 1} η (y / R) δ^{ia}, ℓ z_{R} = 0.

Displayed formulas in this passage

XX-E@1#eq:escaping · line 1379
$h_{ij, R} (t, y) = 2 a (t)^{2} τ (t) R^{- 1} η (y / R) δ_{ij}, h_{00, R} = h_{0 i, R} = φ_{R} = 0.$
unlabeled · line 1374
$η (Y) = Y_{1} ρ (∣ Y ∣) .$
unlabeled · line 1388
$(\calCz_{R})^{ia} = τ (t) R^{- 1} η (y / R) δ^{ia}, ℓ z_{R} = 0.$