Geometrodynamics: the nonlinear dynamics of curved spacetime
K.S. Thorne California Institute of Technology, 1200 East California Boulevard, Pasadena, CA, 91125, USA
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.