Manuscript VII-A-ST@1 · VII-A-ST.tex · section · c39a67a3

Prescribed geometry and the supported Cauchy presentation

Prescribed geometry and the supported Cauchy presentation · lines 249–270

VII-A-ST@1#eq:cone

Fix

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

The physical smooth spacetime is

M = R_{T} \times C_{μ}^{\circ} \times R_{z}, g ˉ = - c^{2} d T^{2} + d r^{2} + α^{2} r^{2} d ϕ^{2} + d z^{2},

where $r > 0$ and $ϕ \in R / (2 π Z)$ . The completion has singular locus

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

It is a worldsheet, not a worldline. No smooth Einstein tensor is asserted on $W$ .

Displayed formulas in this passage

VII-A-ST@1#eq:cone · line 258
$M = R_{T} \times C_{μ}^{\circ} \times R_{z}, g ˉ = - c^{2} d T^{2} + d r^{2} + α^{2} r^{2} d ϕ^{2} + d z^{2},$
unlabeled · line 253
$c > 0, 0 < μ < 2 π, α = 1 - \frac{μ}{2 π} .$
unlabeled · line 265
$W = R_{T} \times {o} \times R_{z} .$