Manuscript I-B@1 · I-B-v1.tex · section · 5357688f

The Einstein comparator

Dynamics without an invented source › The Einstein comparator · lines 1463–1479

The needed statement is the spacetime-constant one CheungXXIIE. The phrase “spatially constant” alone would be insufficient: in units $c = 1$ ,

q = - d T^{2} + e^{2 H T} (d x^{2} + d y^{2} + d z^{2}), H \neq = 0,

is spatially homogeneous but has

R_{00} = - 3 H^{2}, R_{ij} = 3 H^{2} q_{ij}, R = 12 H^{2} .

These follow directly from $Γ^{0}_{ij} = H q_{ij}$ and $Γ^{i}_{0 j} = H δ^{i}_{j}$ .

Displayed formulas in this passage

unlabeled · line 1468
$q = - d T^{2} + e^{2 H T} (d x^{2} + d y^{2} + d z^{2}), H \neq = 0,$
unlabeled · line 1473
$R_{00} = - 3 H^{2}, R_{ij} = 3 H^{2} q_{ij}, R = 12 H^{2} .$