Manuscript XII-F@1 · XII-F.tex · section · 54cb3169

Evaluation of the Einstein row

F3: cancellation on a subclass and a nonzero shell witness › Evaluation of the Einstein row · lines 944–971

XII-F@1#eq:main-w

Define the already handed compact-source response

w_{ξ} = L_{ξ}^{dens} (A γ), e_{ξ} = P E_{0}^{R} w_{ξ} .

This evaluates XII-E's Einstein row. It is not a new application of a propagator to $J_{D}$ .

In the observation dependence region the spatial cutoff is one. By (eq:main-Ab),

w_{ξ}^{00} = 4 a^{'} (t), w_{ξ}^{11} = - 4 a^{'} (t), w_{ξ}^{μν} = 0 otherwise .

Indeed, for a constant diagonal contravariant density and a temporal parameter, its $00$ component acquires $- a^{'} v^{00}$ and its spatial components acquire $+ a^{'} v^{ij}$ .

Set

B (t) = \int_{0}^{t} a (s) d s, C (t) = \int_{0}^{t} (t - s) a (s) d s .

Displayed formulas in this passage

XII-F@1#eq:main-w · line 956
$w_{ξ}^{00} = 4 a^{'} (t), w_{ξ}^{11} = - 4 a^{'} (t), w_{ξ}^{μν} = 0 otherwise .$
unlabeled · line 947
$w_{ξ} = L_{ξ}^{dens} (A γ), e_{ξ} = P E_{0}^{R} w_{ξ} .$
unlabeled · line 967
$B (t) = \int_{0}^{t} a (s) d s, C (t) = \int_{0}^{t} (t - s) a (s) d s .$

Evaluation of the Einstein row

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