The field equations of general relativity are extremely complex. These equations form a system of ten coupled non-linear partial differential equations in four dimensions. When fully expanded in a general coordinate system they have thousands of terms. Thus, if one is interested in studying highly dynamic systems that have little or no symmetry, it is simply impossible to solve the equations exactly and one must fall back on numerical solutions.
Numerical relativity started in the 1960's with the pioneering work of Hahn and Lindquist, but it wasn't until the mid 1970's that the first successful simulations were performed by Smarr and Eppley in the context of the head-on collision of two black holes. Since then numerical relativity has come a long way. The availability of powerful supercomputers, together with an improved understanding of the fundamental theoretical issues that underlie the field, have finally allowed simulations of fully three-dimensional systems with strong and highly dynamical gravitational fields. All this activity has arrived at the right time, as the generation of advanced gravitational wave detectors are finally coming on line. We are living a very exciting stage in the development of this field.

- by Miguel Alcubierre