Manuscript X-A-conv-ST@1 · X-A-conv-ST.tex · section · 8ca47088

Auxiliary coordinates through second order

Stage B: Cauchy solution and regulator preflight › Auxiliary coordinates through second order · lines 601–616

These are the parent Cauchy formulas XConv (:coordcoeff). In particular,

C^{μ} H = S_{ε} (g C^{μ} h + (\partial_{ν} g) [h^{ν μ} - \frac{1}{2} η^{ν μ} tr h]) .

Switch derivatives are retained. The nonlinear expression is $a_{2} (S_{ε} (g h))$ , not $g a_{2} (h)$ or $S_{ε} (g a_{2} (h))$ .

Displayed formulas in this passage

unlabeled · line 606
$C^{μ} H = S_{ε} (g C^{μ} h + (\partial_{ν} g) [h^{ν μ} - \frac{1}{2} η^{ν μ} tr h]) .$