$N+1$ formalism in Einstein-Gauss-Bonnet gravity

Towards the investigation of the full dynamics in a higher-dimensional and/or a stringy gravitational model, we present the basic equations of the Einstein-Gauss-Bonnet gravity theory. We show the $(N+1)$-dimensional version of the Arnowitt-Deser-Misner decomposition including Gauss-Bonnet terms, which shall be the standard approach to treat the space-time as a Cauchy problem. Because of the quasilinear property of the Gauss-Bonnet gravity, we find that the evolution equations can be in a treatable form in numerics. We also show the conformally transformed constraint equations for constructing the initial data. We discuss how the constraints can be simplified by tuning the powers of conformal factors. Our equations can be used both for timelike and spacelike foliations.