Figure 4: Conformal diagram of the critical solution matched to an asymptotically flat one
(RC: regular centre, S: singularity, SSH: self-similarity horizon). Curved lines are lines of constant
coordinate , while converging straight lines are lines of constant coordinate x. Let the initial data
on the Cauchy surface CS be those for the exact critical solution out to the 2-sphere R, and let
these data be smoothly extended to some data that are asymptotically flat, so that the future null
infinity exists. To the past of the matching surface MS the solution coincides with the critical
solution. The spacetime cannot be uniquely continued beyond the Cauchy horizon CH. The redshift
from point A to point B is finite by self-similarity, and the redshift from B to C is finite by asymptotic
flatness.
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