Manuscript VIII-B@3 · VIII-B-v3.tex · remark · 3aa6baa1

Remark: Parameter and kinematical lapse

The retuned polyhedral slicing family › Embedding, acausality, and ordering · lines 878–895

VIII-B@3#rem:lapse

The source clock $s_{c} = - 1/2$ is a parameter value, not a lapse. On a regular branch, the future unit normal is

n = \frac{( 1 , g )}{1 - ∣ g ∣ ^{2}},

so the normal component of the deformation $(\partial_{s} F, 0)$ is

N_{s} = \frac{\partial _{s} F}{1 - ∣ g ∣ ^{2}} .

It equals $3$ on a core branch, $5/2$ on an inner branch, and $1$ on a resting branch. These are local kinematical quantities of this prescribed family. No matter-defined relational clock or relational lapse is constructed. The relational expansion reported in Em02-E CheungEm02E is a different object.

Displayed formulas in this passage

unlabeled · line 882
$n = \frac{( 1 , g )}{1 - ∣ g ∣ ^{2}},$
unlabeled · line 886
$N_{s} = \frac{\partial _{s} F}{1 - ∣ g ∣ ^{2}} .$

Remark: Parameter and kinematical lapse

Displayed formulas in this passage

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