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Einstein Vacuum Equations

NONLINEAR RELATIVISTIC FIELD THEORIES

CONJECTURE 1:

The MGHV extension of any “generic” initial data is inextendible.

CONJECTURE 2:

For “generic” asymptotically flat initial data sets, all singularities are “hidden” by Black Holes.

(M,g) R?? = 0

sc = n/2

Subcritical n < 2
Critical n = 2
Supercritical n > 2

CONJECTURE WP3:

The Einstein Equations are WP for n = 3 and s = sc+1/2 = 2.

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