论文标题
$ d+1 $形式主义在爱因斯坦 - 斯卡尔 - 高斯 - 鲍尼特重力
$d+1$ formalism in Einstein-scalar-Gauss-Bonnet gravity
论文作者
论文摘要
我们介绍了Einstein-Scalar-Gauss-Bonnet（ESGB）的$ d+1 $公式，其中$ d = d+1 $，以及任意（spacelike或Quimelike）切片。我们首先制定了一个行动，将Gibbons-Hawking-York和Myers的动作推广到ESGB理论，表明它们可以用Dirichlet的变化原则来描述。然后，我们将Arnowitt-Deser-Misner（ADM）Lagrangian和Hamiltonian概括为ESGB理论，以及随之而来的$ D+1 $ 1 $分解运动方程。与一般相对论不同，ESGB理论的规范动量在外部曲率中是非线性的。这有两个主要的含义：（i）ADM哈密顿量通常是多亚的，而相关的哈密顿进化是不可预测的； （ii）“ $ d+1 $”运动方程是准线性的，它们可能会以强弯曲的高度动态状态分解。我们的结果对于指导非驱动性方案中ESGB重力的数值相对性的未来发展应该很有用。
We present the $d+1$ formulation of Einstein-scalar-Gauss-Bonnet (ESGB) theories in dimension $D=d+1$ and for arbitrary (spacelike or timelike) slicings. We first build an action which generalizes those of Gibbons-Hawking-York and Myers to ESGB theories, showing that they can be described by a Dirichlet variational principle. We then generalize the Arnowitt-Deser-Misner (ADM) Lagrangian and Hamiltonian to ESGB theories, as well as the resulting $d+1$ decomposition of the equations of motion. Unlike general relativity, the canonical momenta of ESGB theories are nonlinear in the extrinsic curvature. This has two main implications: (i) the ADM Hamiltonian is generically multivalued, and the associated Hamiltonian evolution is not predictable; (ii) the "$d+1$" equations of motion are quasilinear, and they may break down in strongly curved, highly dynamical regimes. Our results should be useful to guide future developments of numerical relativity for ESGB gravity in the nonperturbative regime.
