Manuscript IX-D-ST@1 · IX-D-ST.tex · section · b1dc631a

A specified flat realization and the solid-ball correction

A specified flat realization and the solid-ball correction · lines 1962–1981

IX-D-ST@1#eq:Eflat

The following is a diagnostic realization, not a replacement of an unspecified inherited operator. Let

(C h)^{μ} = \partial_{ν} h^{μν} - \frac{1}{2} \partial^{μ} (η^{α β} h_{α β}),

and define the componentwise flat zero-Cauchy response

(E_{fl} j) (t, x) = \int_{0}^{t} \int_{R^{3}} \frac{δ ( t - v - ∣ x - w ∣ )}{4 π ∣ x - w ∣} j (v, w) d^{3} w d v .

All applications are supported inside the retained chart.

Displayed formulas in this passage

IX-D-ST@1#eq:Eflat · line 1972
$(E_{fl} j) (t, x) = \int_{0}^{t} \int_{R^{3}} \frac{δ ( t - v - ∣ x - w ∣ )}{4 π ∣ x - w ∣} j (v, w) d^{3} w d v .$
unlabeled · line 1967
$(C h)^{μ} = \partial_{ν} h^{μν} - \frac{1}{2} \partial^{μ} (η^{α β} h_{α β}),$