Construction of Cauchy Data of Vacuum Einstein field equations Evolving to Black Holes

2012/07/13 by Junbin Li, Li, Junbin, Pin Yu +1
Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory

paper · pdf · doi:10.48550/arxiv.1207.3164

openalex publication_date 2012/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 constructions of initial data set.

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