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

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

2008-10-10

arxiv.org/abs/0810.1790v1

Phys.Rev.D78:084037,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15pages, no figure, to appear in PRD

Scientific paper

10.1103/PhysRevD.78.084037

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.

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