What is numerical relativity?

General relativity – Einstein's theory of relativistic gravitation – is the cornerstone of modern cosmology, the physics of neutron stars and black holes, the generation of gravitational radiation, and countless other cosmic phenomena in which strong-field gravitation plays a dominant role. Yet the theory remains largely untested, except in the weak-field, slow-velocity regime. Moreover, solutions to Einstein's equations, except for a few idealized cases characterized by high degrees of symmetry, have not been obtained as yet for many of the important dynamical scenarios thought to occur in nature. With the advent of supercomputers, it is now possible to tackle these complicated equations numerically and explore these scenarios in detail. That is the main goal of numerical relativity, the art and science of developing computer algorithms to solve Einstein's equations for astrophysically realistic, high-velocity, strong-field systems.

Numerical relativity has become one of the most powerful probes of relativistic spacetimes. It is the tool that allows us to recreate cataclysmic cosmic phenomena that are otherwise inaccessible in the conventional laboratory – like gravitational collapse to black holes and neutron stars, the inspiral and coalescence of binary black holes and neutron stars, and the generation and propagation of gravitational waves, to name a few. Numerical relativity picks up where post-Newtonian theory and general relativistic perturbation theory leave off. It enables us to follow the full nonlinear growth of relativistic instabilities and determine the final fate of unstable systems.