"Any strongly asymptotically flat, maximal initial data set that satisfies the global smallness assump tion, stated in the introduction, leads to a unique, globally hyperbolic, smooth, and geodesically complete solution of the Einstein-Vacuum equations, which is foliated by a normal maximal time function t, defined for all t > —1."
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I'm thinking this...
@ACuriousMind Ahhhhh, $S^2$ is complete (in the Riemannian sense) by Hopf-Rinow since a compact metric space is complete (in the topological sense), right?
The master thesis by J. Hartong, On problems in de Sitter spacetime physics has some detailed explanation from Eq 2.5 to 2.6. I was able to get the final answer following his notes.
Two important intermediate steps are:
$\partial_aZ=-l^{-2}(\frac{X^d(y)}{X^d(x)}X_a(x)-X_a(y))$
and
$(\partial...
@Danu I like how this guy did 6 pages of calculations and was ignored
@Slereah oh no, without the singularity
just extend past the horizon
I wonder...can you argue that the exterior is glob hyp and the interior is glob hyp
The master thesis by J. Hartong, On problems in de Sitter spacetime physics has some detailed explanation from Eq 2.5 to 2.6. I was able to get the final answer following his notes.
Two important intermediate steps are:
$\partial_aZ=-l^{-2}(\frac{X^d(y)}{X^d(x)}X_a(x)-X_a(y))$
and
$(\partial...
