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Published 2014 | public
Journal Article

Geometrodynamics: the nonlinear dynamics of curved spacetime


We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of spacetime curvature near singularities, the instability of black strings in five spacetime dimensions, and the collision of four-dimensional black holes. We also discuss the prospects for further discoveries in geometrodynamics via observations of gravitational waves.

Additional Information

© 2014 Uspekhi Fizicheskikh Nauk, Russian Academy of Sciences. Received 9 January 2014. We are grateful to Thorne's dear friend, the late Leonid Petrovich Grishchuk, for urging us to write this review article, and for many stimulating discussions. We thank members of the SXS collaboration and of the Caltech/ Cornell Vortex/Tendex research group for data used for figures in Section 5 and for the work that made much of that section possible. We gratefully acknowledge support from the Sherman Fairchild Foundation, the Brinson Foundation, and NSF grants PHY-106881 and AST-1333520.

Additional details

August 19, 2023
October 17, 2023