科研之友
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摘要
In this note we perform the n + 1 decomposition, or Arnowitt-Deser-Misner (ADM) formulation of f(Lovelock) gravity theory. The Hamiltonian form of Lovelock gravity was known since the work of Teitelboim and Zanelli in 1987, but this result had not yet been extended to f(Lovelock) gravity. Besides, field equations of f(Lovelock) have been recently computed by Bueno et al, though without ADM decomposition.
We focus on the non-degenerate case. i.e. when the Hessian of f is invertible. Using the same Legendre transform as for f(R) theories, we can identify the partial derivatives off as scalar fields, and consider the theory as a generalised scalar-tensor theory. We then derive the field equations, and project them along a n + 1 decomposition. We obtain an original system of constraint equations for f(Lovelock) gravity, as well as dynamical equations. We give explicit formulas for the f(R, Gauss-Bonnet) case.
- 出版日期2018-6-7
