# Geometrodynamics: The Nonlinear Dynamics of Curved Spacetime

## TL;DR

This paper reviews recent advances in the nonlinear dynamics of curved spacetime, highlighting phenomena like gravitational collapse, black hole interactions, and the potential for gravitational wave observations to reveal new insights.

## Contribution

It provides a comprehensive overview of key discoveries in geometrodynamics made through numerical solutions of Einstein's equations, emphasizing phenomena and future observational prospects.

## Key findings

- Critical phenomena and self-similarity in gravitational collapse
- Instability of black strings in higher dimensions
- Black hole collision dynamics and gravitational wave prospects

## 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.