Manuscript Em02-E@1 · Em02-E-v1.tex · section · f3795050

Clock-adapted description

Clock slices and harmonic spatial labels › Clock-adapted description · lines 437–457

Let

Ψ_{λ} (s, x) = (τ_{λ} (s, x), x) .

The induced positive spatial metric on the clock slice is

q_{λ, ij} = g_{λ, μν} (Ψ_{λ}) \partial_{i} Ψ_{λ}^{μ} \partial_{j} Ψ_{λ}^{ν} .

Write

q_{λ, ij} = a^{2} δ_{ij} + λ q_{1, ij} + \frac{λ ^{2}}{2} q_{2, ij} .

Displayed formulas in this passage

unlabeled · line 440
$Ψ_{λ} (s, x) = (τ_{λ} (s, x), x) .$
unlabeled · line 444
$q_{λ, ij} = g_{λ, μν} (Ψ_{λ}) \partial_{i} Ψ_{λ}^{μ} \partial_{j} Ψ_{λ}^{ν} .$
unlabeled · line 451
$q_{λ, ij} = a^{2} δ_{ij} + λ q_{1, ij} + \frac{λ ^{2}}{2} q_{2, ij} .$