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Black hole formation and stability: A mathematical investigation


Author: Lydia Bieri
Journal: Bull. Amer. Math. Soc.
MSC (2010): Primary 83C05, 83C57, 35A20, 35A01, 35A02, 53C10
DOI: https://doi.org/10.1090/bull/1592
Published electronically: September 25, 2017
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Abstract: The dynamics of the Einstein equations feature the formation of black holes. These are related to the presence of trapped surfaces in the spacetime manifold. The mathematical study of these phenomena has gained momentum since D. Christodoulou's breakthrough result proving that, in the regime of pure general relativity, trapped surfaces form through the focusing of gravitational waves. (The latter were observed for the first time in 2015 by Advanced LIGO.) The proof combines new ideas from geometric analysis and nonlinear partial differential equations, and it introduces new methods to solve large data problems. These methods have many applications beyond general relativity. D. Christodoulou's result was generalized by S. Klainerman and I. Rodnianski, and more recently by these authors and J. Luk. Here, we investigate the dynamics of the Einstein equations, focusing on these works. Finally, we address the question of stability of black holes and what has been known so far, involving recent works of many contributors.


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Additional Information

Lydia Bieri
Affiliation: University of Michigan, Department of Mathematics, Ann Arbor, Michigan
Email: lbieri@umich.edu

DOI: https://doi.org/10.1090/bull/1592
Received by editor(s): April 27, 2017
Published electronically: September 25, 2017
Additional Notes: The author acknowledges her NSF support and is supported by NSF CAREER Grant No. DMS-1253149.
Article copyright: © Copyright 2017 American Mathematical Society