PPT Slide
Einstein Vacuum Equations
NONLINEAR RELATIVISTIC FIELD THEORIES
The MGHV extension of any “generic” initial data is inextendible.
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
Solutions are either geodesically
complete or, if incomplete,
end up in curvature singularities.
The Einstein Equations are WP for n = 3 and s = sc+1/2 = 2.
What is the optimal exponent s ? sc such
that the initial value problem is WP in Hs