Construction of Cauchy data of vacuum Einstein field equations evolving to black holes


We show the existence of complete, asymptotically flat Cauchy initial data for the vacuum Einstein field equations, free of trapped surfaces, whose future development must admit a trapped surface. Moreover, the datum is exactly a constant time slice in Minkowski space-time inside and exactly a constant time slice in Kerr space-time outside.
The proof makes use of the full strength of Christodoulou’s work on the dynamical formation of black holes and Corvino-Schoen’s work on the construction of initial data sets.


Junbin Li

Department of Mathematics, Sun Yat-sen University Guangzhou, China

Pin Yu

Mathematical Sciences Center, Tsinghua University Beijing, China