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 5 spacetime dimensions, and the collision of four-dimensional black holes. We also discuss the prospects for further discoveries in geometrodynamics via observation of gravitational waves.

PACS: 04.20.−q, 04.25.dg, 04.25.dc, 04.50.Gh (all) DOI: 10.3367/UFNe.0184.201404b.0367 URL: https://ufn.ru/en/articles/2014/4/c/ 000338713200002 2-s2.0-84904013780 2014PhyU...57..342S Citation: Scheel M A, Thorne K S "Geometrodynamics: the nonlinear dynamics of curved spacetime" Phys. Usp. 57 342–351 (2014) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 9th, January 2014, accepted: 10th, January 2014 Оригинал: Шил М А, Торн К С «Геометродинамика: нелинейная динамика искривлённого пространства-времени» УФН 184 367–378 (2014); DOI: 10.3367/UFNr.0184.201404b.0367