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The numerical evolution of Einstein's field equations in a generic backgroundhas the potential to answer a variety of important questions in physics: fromapplications to the gauge-gravity duality, to modelling black hole productionin TeV gravity scenarios, analysis of the stability of exact solutions andtests of Cosmic Censorship. In order to investigate these questions, we extendnumerical relativity to more general space-times than those investigatedhitherto, by developing a framework to study the numerical evolution of Ddimensional vacuum space-times with an SO(D-2) isometry group for D\ge 5, orSO(D-3) for D\ge 6.  Performing a dimensional reduction on a (D-4)-sphere, the D dimensionalvacuum Einstein equations are rewritten as a 3+1 dimensional system with sourceterms, and presented in the Baumgarte, Shapiro, Shibata and Nakamura (BSSN)formulation. This allows the use of existing 3+1 dimensional numerical codeswith small adaptations. Brill-Lindquist initial data are constructed in Ddimensions and a procedure to match them to our 3+1 dimensional evolutionequations is given. We have implemented our framework by adapting the LEAN codeand perform a variety of simulations of non-spinning black hole space-times.Specifically, we present a modified moving puncture gauge which facilitateslong term stable simulations in D=5. We further demonstrate the internalconsistency of the code by studying convergence and comparing numerical versusanalytic results in the case of geodesic slicing for D=5,6.

Numerical relativity for D dimensional axially symmetric space-times: formalism and code tests