论文标题
Lovelock Gravity的一阶Lagrangian和Hamiltonian
First-order Lagrangian and Hamiltonian of Lovelock gravity
论文作者
论文摘要
基于多年来许多作者在爱因斯坦 - 希尔伯特，高斯 - 邦纳特和洛夫洛克重力拉格朗日的结构中获得的洞察力，我们展示了如何以基本方式得出 - 他们的一阶，普遍的“ ADM” Lagrangian和相关的汉密尔顿。为此，我们从补充了Myers边界术语的Lovelock Lagrangian开始，该术语保证了dirichlet差异原理，其表面$π^{ij}ΔH_{ij {ij} $的表面术语，其中$π^{ij} $是经典的conjugate conjugate conjugate to Bargunical conjugate to Bargue of Boundary of Bourdinal $ h________}然后，一阶拉格朗日密度是通过公制衍生$ \ partial_wh_ {ij} $正常的$π^{ij} $集成到边界上的$π^{ij} $获得的，或者通过将迈尔斯术语重写为批量项。
Based on the insight gained by many authors over the years on the structure of the Einstein-Hilbert, Gauss-Bonnet and Lovelock gravity Lagrangians, we show how to derive -- in an elementary fashion -- their first-order, generalized "ADM" Lagrangian and associated Hamiltonian. To do so, we start from the Lovelock Lagrangian supplemented with the Myers boundary term, which guarantees a Dirichlet variational principle with a surface term of the form $π^{ij}δh_{ij}$, where $π^{ij}$ is the canonical momentum conjugate to the boundary metric $h_{ij}$. Then, the first-order Lagrangian density is obtained either by integration of $π^{ij}$ over the metric derivative $\partial_wh_{ij}$ normal to the boundary, or by rewriting the Myers term as a bulk term.
