Numerical integration of Einstein's field equations - art. no. 024007

Many numerical codes now under development to solve Einstein's equations of general relativity in (3 + 1)-dimensional spacetimes employ the standard A DM form of the held equations. This form involves evolution equations for t he raw spatial metric and extrinsic curvature tensors. Following Shibata an d Nakamura, we modify these equations by factoring out the conformal factor and introducing three "connection functions." The evolution equations can then be reduced to wave equations for the conformal metric components, whic h are coupled to evolution equations for the connection functions. We evolv e small amplitude gravitational waves and make a direct comparison of the n umerical performance of the modified equations with the standard ADM equati ons. We find that the modified form exhibits much improved stability. [S005 6-2821(98)08124-7].