Manuscript IX-A@1 · IX-A.tex · section · 55aa6f6d

No hidden equation-of-motion quotient

Boundary and topology audit › No hidden equation-of-motion quotient · lines 1998–2015

For every smooth off-shell metric,

h = U (γ_{0} h, γ_{1} h) + E_{0} □_{η} h

on the future half-space. This is the ordinary Cauchy reconstruction identity. It does not set $□_{η} h$ to zero.

Likewise, a replacement

q_{a} ⟼ q_{a} + □_{η} r

does not preserve the functional on all smooth metrics unless $□_{η} r = 0$ as a distribution. On-shell equality is a different equivalence relation and is not used in this manuscript.

Displayed formulas in this passage

unlabeled · line 2001
$h = U (γ_{0} h, γ_{1} h) + E_{0} □_{η} h$
unlabeled · line 2009
$q_{a} ⟼ q_{a} + □_{η} r$