Manuscript XIX-A@1 · XIX-A.tex · section · e30d8062

The ramp changes the first harmonic response

Third refusal: the density ramp is a named non-clock › The ramp changes the first harmonic response · lines 1100–1115

XIX-A@1#eq:pure-gauge-density

Let $ξ$ be a compact smooth vector field vanishing in an initial collar, and set

(K ξ)_{μν} = \partial_{μ} ξ_{ν} + \partial_{ν} ξ_{μ} .

For the first metric-density coefficient,

\partial_{α} A_{1}^{α μ} [K ξ] = - □_{η} ξ^{μ} .

Let $G_{C}$ denote the zero-Cauchy solution operator for $□_{η}$ on the slab.

Displayed formulas in this passage

XIX-A@1#eq:pure-gauge-density · line 1108
$\partial_{α} A_{1}^{α μ} [K ξ] = - □_{η} ξ^{μ} .$
unlabeled · line 1104
$(K ξ)_{μν} = \partial_{μ} ξ_{ν} + \partial_{ν} ξ_{μ} .$