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

The prescribed host and its causal geometry

The prescribed host and its causal geometry · lines 202–218

Choose an origin $T_{Σ}$ and put

t = c (T - T_{Σ}), q = h + d z^{2}, d V = α r d r d φ d z .

Thus

g = - d t^{2} + q, d vol_{g} = d t d V .

All propagation times and lengths below are measured in these $t$ -units. A time bound in the $T$ -coordinate is obtained by division by $c$ .

Displayed formulas in this passage

unlabeled · line 205
$t = c (T - T_{Σ}), q = h + d z^{2}, d V = α r d r d φ d z .$
unlabeled · line 211
$g = - d t^{2} + q, d vol_{g} = d t d V .$