Manuscript I-B-G@2 · I-B-G-v2.tex · assumption · 3b4d700f

Assumption: Prescribed I-B geometry

The prescribed host and its causal geometry · lines 176–202

I-B-G@2#ass:host

Fix

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

The regular spatial cone and the regular spacetime are

C_{μ}^{\circ} = (0, \infty) \times (R /2 π Z), h = d r^{2} + α^{2} r^{2} d φ^{2},

N = C_{μ}^{\circ} \times R_{z}, M = R_{T} \times N, g = - c^{2} d T^{2} + h + d z^{2} .

The metric completion adds the apex worldsheet

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

but $W$ is not part of $M$ . The opening angle is $2 π α = 2 π - μ$ . These are the prescribed background data of I-B CheungIB.

Displayed formulas in this passage

unlabeled · line 179
$0 < μ < 2 π, α = 1 - \frac{μ}{2 π} \in (0, 1), c > 0, m \geq 0.$
unlabeled · line 185
$C_{μ}^{\circ} = (0, \infty) \times (R /2 π Z), h = d r^{2} + α^{2} r^{2} d φ^{2},$
unlabeled · line 189
$N = C_{μ}^{\circ} \times R_{z}, M = R_{T} \times N, g = - c^{2} d T^{2} + h + d z^{2} .$
unlabeled · line 195
$W = R_{T} \times {o} \times R_{z},$