Construction of Cauchy data of vacuum Einstein field equations evolving to black holes. (English) Zbl 1321.83011

The authors construct Cauchy initial data for the Einstein equations free of trapped surfaces that upon time development lead to the formation of trapped surfaces. The initial data is such that the interior of a ball is a constant time slice of Minkowski space time and the exterior is a constant time slice of the Kerr metric in Boyer-Lindquist coordinates. In between are two concentric shells one filled with a constant time slice of the Schwarzschild space time and the other with D. Christodoulou’s short pulse ansatz [The formation of black holes in general relativity. Zürich: European Mathematical Society (EMS) (2009; Zbl 1197.83004)]. The regions are patched with Corvino and Schoen’s gluing [J. Corvino and R. M. Schoen, J. Differ. Geom. 73, No. 2, 185–217 (2006; Zbl 1122.58016)].


83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C57 Black holes
35Q76 Einstein equations
83C75 Space-time singularities, cosmic censorship, etc.
Full Text: DOI arXiv


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