(ed.). Gravitational waves (IOP, 2001)(422s).

Chapter 18Numerical relativityGeneral relativity is the fundamental theory of gravity, which is governedby an extremely complex set of coupled, nonlinear, hyperbolic-elliptic partialdifferential equations. General solutions to these equations, needed to fullyunderstand their implications as a fundamental theory of physics, are elusive.Additionally, the astrophysics of compact objects, which requires Einstein’stheory of general relativity for understanding phenomena such as black holesand neutron stars, is attracting increasing attention. The largest parallelsupercomputers are finally approaching the speed and memory required to solvethe complete set of Einstein’s equations for the first time since they were writtenover 80 years ago, allowing one to attempt full 3D simulations of such excitingevents as colliding black holes and neutron stars. In this paper we review thecomputational effort in this direction, and discuss a new 3D multipurpose parallelcode called ‘Cactus’ for general relativistic astrophysics. Directions for furtherwork are indicated where appropriate.18.1 OverviewThis article is intended to provide an introduction and overview to numericalrelativity, following a set of lectures given at the Como SIGRAV School ongravitational waves in Spring, 1999. We have based them heavily on severalprevious articles, especially [1, 2], but we have tried to extend and update themwhere significant new work has been done.The Einstein equations for the structure of spacetime have remainedessentially unchanged since their discovery nearly a century ago, providing theunderpinnings of modern theories of gravity, astrophysics and cosmology. Thetheory is essential in describing phenomena such as black holes, compact objects,supernovae, and the formation of structure in the universe. Unfortunately, theequations are a set of highly complex, coupled, nonlinear partial differentialequations involving ten functions of four independent variables. They are amongthe most complicated equations in mathematical physics. For this reason, in361