Manuscript IX-B-ST@1 · IX-B-ST.tex · section · f6af1523

Prescribed cone and supported regular laboratory

Prescribed cone and supported regular laboratory · lines 256–285

IX-B-ST@1#eq:host

Use $δ_{c}$ for the conical deficit and $μ$ for the numerical subtraction scale. Fix

0 < δ_{c} < 2 π, α = 1 - \frac{δ _{c}}{2 π}, c > 0.

The host is

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

The angular coordinate has period $2 π$ . The stipulated completion has defect

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

This is a worldsheet; only fixed- $z$ sections are worldlines. The signature is $(-, +, +, +)$ , the lapse in $T$ is one, and static proper time is $T$ . These are I-B inputs, not outputs of the calibration CheungIB.

Displayed formulas in this passage

IX-B-ST@1#eq:host · line 266
$M_{δ_{c}} = R_{T} \times C_{δ_{c}}^{\circ} \times R_{z}, g_{δ_{c}} = - c^{2} d T^{2} + d r^{2} + α^{2} r^{2} d φ^{2} + d z^{2}, r > 0.$
unlabeled · line 261
$0 < δ_{c} < 2 π, α = 1 - \frac{δ _{c}}{2 π}, c > 0.$
unlabeled · line 277
$W = R_{T} \times {o} \times R_{z} .$

Prescribed cone and supported regular laboratory

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