5.2 Stability of Minkowski space5 Global existence for small 5 Global existence for small

5.1 Stability of de Sitter space

  In [69] Friedrich proved a result on the stability of de Sitter space. This concerns the Einstein vacuum equations with positive cosmological constant. His result is as follows. Consider initial data induced by de Sitter space on a regular Cauchy hypersurface. Then all initial data (vacuum with positive cosmological constant) near enough to these data in a suitable (Sobolev) topology have maximal Cauchy developments which are geodesically complete. In fact the result gives much more detail on the asymptotic behaviour than just this and may be thought of as proving a form of the cosmic no hair conjecture in the vacuum case. (This conjecture says roughly that the de Sitter solution is an attractor for expanding cosmological models with positive cosmological constant.) This result is proved using conformal techniques and, in particular, the regular conformal field equations developed by Friedrich.

There are results obtained using the regular conformal field equations for negative or vanishing cosmological constant [71, 74Jump To The Next Citation Point In The Article] but a detailed discussion of their nature would be out of place here. (Cf. however section  7.1 .)



5.2 Stability of Minkowski space5 Global existence for small 5 Global existence for small

image Local and Global Existence Theorems for the Einstein Equations
Alan D. Rendall
http://www.livingreviews.org/lrr-2000-1
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