Manuscript XVI-O1-ST@5 · XVI-O1-ST-v5.tex · section · dd45e0d1

The prescribed host and analytical carrier

The prescribed host and analytical carrier · lines 293–316

XVI-O1-ST@5#eq:host

Fix $0 < μ < 2 π$ , $a = 1 - μ / (2 π)$ , and $c_{host} > 0$ . Set

C_{μ}^{\circ} = (0, \infty)_{r} \times (R /2 π Z)_{ϑ}, M^{\circ} = R_{T} \times C_{μ}^{\circ} \times R_{z},

with prescribed metric

G = - c_{host}^{2} d T^{2} + d r^{2} + a^{2} r^{2} d ϑ^{2} + d z^{2} .

Increasing $T$ is future directed. The completion defect is

W = R_{T} \times {o} \times R_{z} .

The supported laboratory avoids $W$ ; the inherited width $ϵ > 0$ remains fixed CheungIB,CheungXAST.

Displayed formulas in this passage

XVI-O1-ST@5#eq:host · line 304
$G = - c_{host}^{2} d T^{2} + d r^{2} + a^{2} r^{2} d ϑ^{2} + d z^{2} .$
unlabeled · line 298
$C_{μ}^{\circ} = (0, \infty)_{r} \times (R /2 π Z)_{ϑ}, M^{\circ} = R_{T} \times C_{μ}^{\circ} \times R_{z},$
unlabeled · line 310
$W = R_{T} \times {o} \times R_{z} .$