Manuscript V-B@1 · V-B-v1.tex · section · 3fadc1ad

Geometry, local interpretation, and analytical continuation

Geometry, local interpretation, and analytical continuation · lines 241–260

Thus a global wave theorem cannot be transferred merely from local flatness. The standard global Green theory requires an appropriate globally hyperbolic domain BGP.

Choose a regular developing chart

χ : U ⟶ B_{R} \subset R^{3}

and a reference time $T_{0}$ . Write

t = c (T - T_{0}), x = χ (r, ϕ, z) .

The local metric becomes

η = - d t^{2} + d x^{2}, η_{μν} = \diag (- 1, 1, 1, 1) .

Displayed formulas in this passage

unlabeled · line 248
$χ : U ⟶ B_{R} \subset R^{3}$
unlabeled · line 252
$t = c (T - T_{0}), x = χ (r, ϕ, z) .$
unlabeled · line 256
$η = - d t^{2} + d x^{2}, η_{μν} = \diag (- 1, 1, 1, 1) .$

Nearby in this section

section: Geometry, local interpretation, and analytical continuation
proposition: Proposition: The full regular cone is not globally hyperbolic
definition: Definition: Presentation and laboratory contract
section: Geometry, local interpretation, and analytical continuation
lemma: Lemma: Local causal interpretation
section: Geometry, local interpretation, and analytical continuation