Manuscript I-B-VP@3 · I-B-VP-v3.tex · assumption · 93c04eb4

Assumption: Prescribed background

Host, bundle, field normalization, and signature · lines 362–386

I-B-VP@3#ass:host

Fix

0 < μ < 2 π, α = 1 - \frac{μ}{2 π} \in (0, 1) .

The regular spacetime is

M = R_{t} \times (0, \infty)_{r} \times (R /2 π Z)_{φ} \times R_{z},

with

g = - d t^{2} + d r^{2} + α^{2} r^{2} d φ^{2} + d z^{2} .

The metric completion adds $W = {r = 0}$ , but $W \neq \subset M$ . We use $ℏ = c = 1$ , and $t$ is length-valued time.

The massless equation is

P Φ = (- □_{g} + ξ R) Φ = (\partial_{t}^{2} + B) Φ = 0.

On $M$ , $R = 0$ . No distributional apex curvature coupling is included.

Displayed formulas in this passage

unlabeled · line 365
$0 < μ < 2 π, α = 1 - \frac{μ}{2 π} \in (0, 1) .$
unlabeled · line 369
$M = R_{t} \times (0, \infty)_{r} \times (R /2 π Z)_{φ} \times R_{z},$
unlabeled · line 374
$g = - d t^{2} + d r^{2} + α^{2} r^{2} d φ^{2} + d z^{2} .$
unlabeled · line 381
$P Φ = (- □_{g} + ξ R) Φ = (\partial_{t}^{2} + B) Φ = 0.$