×
Li, Junbin; Yu, Pin

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

Ann. Math. (2) 181, No. 2, 699-768 (2015).
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)].
Reviewer: Jorge Pullin (Baton Rouge)

Cited in 11 Documents

MSC:

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

Keywords:

Einstein constraints equations; black holes

Citations:

Zbl 1197.83004; Zbl 1122.58016
PDF BibTeX XML Cite
\textit{J. Li} and \textit{P. Yu}, Ann. Math. (2) 181, No. 2, 699--768 (2015; Zbl 1321.83011)
Full Text: DOI arXiv
  • logo of hbz
  • logo of WorldCat

References:

[1] D. Christodoulou, ”The formation of black holes and singularities in spherically symmetric gravitational collapse,” Comm. Pure Appl. Math., vol. 44, iss. 3, pp. 339-373, 1991. · Zbl 0728.53061
[2] D. Christodoulou, The Formation of Black Holes in General Relativity, Zürich: European Mathematical Society (EMS), 2009. · Zbl 1197.83004
[3] D. Christodoulou and S. Klainerman, The Global Nonlinear Stability of the Minkowski Space, Princeton, NJ: Princeton Univ. Press, 1993, vol. 41. · Zbl 0827.53055
[4] J. Corvino, ”Scalar curvature deformation and a gluing construction for the Einstein constraint equations,” Comm. Math. Phys., vol. 214, iss. 1, pp. 137-189, 2000. · Zbl 1031.53064
[5] J. Corvino and R. M. Schoen, ”On the asymptotics for the vacuum Einstein constraint equations,” J. Differential Geom., vol. 73, iss. 2, pp. 185-217, 2006. · Zbl 1122.58016
[6] S. Klainerman and I. Rodnianski, ”Ricci defects of microlocalized Einstein metrics,” J. Hyperbolic Differ. Equ., vol. 1, iss. 1, pp. 85-113, 2004. · Zbl 1063.53051
[7] S. Klainerman and I. Rodnianski, ”Causal geometry of Einstein-vacuum spacetimes with finite curvature flux,” Invent. Math., vol. 159, iss. 3, pp. 437-529, 2005. · Zbl 1136.58018
[8] S. Klainerman and I. Rodnianski, ”Rough solutions of the Einstein-vacuum equations,” Ann. of Math., vol. 161, iss. 3, pp. 1143-1193, 2005. · Zbl 1089.83006
[9] S. Klainerman and I. Rodnianski, ”The causal structure of microlocalized rough Einstein metrics,” Ann. of Math., vol. 161, iss. 3, pp. 1195-1243, 2005. · Zbl 1089.83007
[10] S. Klainerman and I. Rodnianski, ”Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux,” Geom. Funct. Anal., vol. 16, iss. 1, pp. 164-229, 2006. · Zbl 1206.35081
[11] S. Klainerman and I. Rodnianski, ”On the formation of trapped surfaces,” Acta Math., vol. 208, iss. 2, pp. 211-333, 2012. · Zbl 1246.83028
[12] J. Luk, ”On the local existence for the characteristic initial value problem in general relativity,” Int. Math. Res. Not., vol. 2012, iss. 20, p. no. 20, 4625-4678. · Zbl 1262.83011
[13] A. D. Rendall, ”Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations,” Proc. Roy. Soc. London Ser. A, vol. 427, iss. 1872, pp. 221-239, 1990. · Zbl 0701.35149
[14] M. Reiterer and E. Trubowitz, ”Strongly focused gravitational waves,” Comm. Math. Phys., vol. 307, iss. 2, pp. 275-313, 2011. · Zbl 1229.83027
[15] R. Schoen and S. T. Yau, ”The existence of a black hole due to condensation of matter,” Comm. Math. Phys., vol. 90, iss. 4, pp. 575-579, 1983. · Zbl 0541.53054
[16] S. T. Yau, ”Geometry of three manifolds and existence of black hole due to boundary effect,” Adv. Theor. Math. Phys., vol. 5, iss. 4, pp. 755-767, 2001. · Zbl 1019.53016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.