Manuscript IX-C-ST@1 · IX-C-ST.tex · section · 892f50c4

The prescribed host and the supported laboratory

The prescribed host and the supported laboratory · lines 250–277

IX-C-ST@1#eq:host

Fix a deficit $0 < δ_{c} < 2 π$ , set

α = 1 - \frac{δ _{c}}{2 π},

and fix a conversion speed $c_{light} > 0$ . The regular host is the prescribed product

M_{δ_{c}} = R_{T} \times C_{δ_{c}}^{\circ} \times R_{z}, g_{δ_{c}} = - c_{light}^{2} d T^{2} + d r^{2} + α^{2} r^{2} d φ^{2} + d z^{2}, r > 0,

with $φ$ periodic of period $2 π$ . The stipulated completion has defect

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

It is a worldsheet, not a worldline. The lapse in $T$ is one; static proper time is $T$ . These data are prescribed, as in I-B IB.

Displayed formulas in this passage

IX-C-ST@1#eq:host · line 259
$M_{δ_{c}} = R_{T} \times C_{δ_{c}}^{\circ} \times R_{z}, g_{δ_{c}} = - c_{light}^{2} d T^{2} + d r^{2} + α^{2} r^{2} d φ^{2} + d z^{2}, r > 0,$
unlabeled · line 254
$α = 1 - \frac{δ _{c}}{2 π},$
unlabeled · line 271
$W = R_{T} \times {o} \times R_{z} .$