Manuscript VII-F-ST@1 · VII-F-ST.tex · section · 9eee7a44

The exact transverse family and its product lift

The exact transverse family and its product lift · lines 340–368

VII-F-ST@1#eq:family, VII-F-ST@1#eq:lift

The following functions reproduce the source family CheungVIIF (:family):

ρ = ξ + η, h = \frac{2}{3} (ξ + η), k = \frac{3}{5} min {ξ, η}, F_{s} = s + min {2, max {h, s + k}}, - 1 \leq s \leq 1.

They agree on identified rays: there $ρ = r / ℓ$ , $h = 2 ρ /3$ , and $k = 0$ . Consequently $F_{s}$ is a single-valued continuous function on the completed transverse cone.

Define the $3 + 1$ -dimensional markings

Σ_{s} = {(T, x, z) : T = T_{*} + \frac{ℓ}{c} F_{s} (x / ℓ), z \in R} .

Only the supported slab of Definition def:support and the separately specified regular laboratory are operationally used.

Displayed formulas in this passage

VII-F-ST@1#eq:family · line 345
$ρ = ξ + η, h = \frac{2}{3} (ξ + η), k = \frac{3}{5} min {ξ, η}, F_{s} = s + min {2, max {h, s + k}}, - 1 \leq s \leq 1.$
VII-F-ST@1#eq:lift · line 360
$Σ_{s} = {(T, x, z) : T = T_{*} + \frac{ℓ}{c} F_{s} (x / ℓ), z \in R} .$

The exact transverse family and its product lift

Displayed formulas in this passage

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