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

TL;DR

This paper derives the $(N+1)$-dimensional ADM formalism for Einstein-Gauss-Bonnet gravity, enabling numerical and initial data analysis in higher-dimensional and string-inspired gravitational models.

Contribution

It presents the first detailed $(N+1)$-dimensional ADM decomposition including Gauss-Bonnet terms, suitable for numerical evolution and initial data construction in higher-dimensional gravity.

Findings

Derived treatable evolution equations for Gauss-Bonnet gravity.

Provided conformally-transformed constraint equations for initial data.

Discussed simplification of constraints via conformal factor tuning.

Abstract

Towards the investigation of the full dynamics in higher-dimensional and/or stringy gravitational model, we present the basic equations of the Einstein-Gauss-Bonnet gravity theory. We show $(N+1)$-dimensional version of the ADM decomposition including Gauss-Bonnet terms, which shall be the standard approach to treat the space-time as a Cauchy problem. Due to the quasi-linear 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 an 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.