Geometrodynamics: The Nonlinear Dynamics of Curved Spacetime

Abstract

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.

arXiv comment12 pages, 14 figures. Published in 2014 in Uspekhi Fizicheskikh Nauk and P N Lebedev Physics Institute of the Russian Academy of Sciences in an issue commemorating the 100th anniversary of the birth of Y B Zeldovich

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Cited by in corpus (10)

• Silhouettes of invisible black holes
• Strong gravitational lensing by a strongly naked null singularity
• Dynamics of critical collapse
• Strength of the naked singularity in critical collapse
• Numerical Relativity Beyond Astrophysics
• Post-Newtonian Lagrangian of an N-body System with Arbitrary Mass and Spin Multipoles
• Entanglement and squeezing of gravitational waves
• Temporary Singularities and Axions: an analytic solution that challenges charge conservation
• Nonlinear Ringdowns as Sources and Detectors of Quantum Gravitational Waves
• Dynamics near the central singularity in spherical collapse