SOLVING THE HAMILTON-JACOBI EQUATION FOR GENERAL-RELATIVITY

被引:77
作者
PARRY, J [1 ]
SALOPEK, DS [1 ]
STEWART, JM [1 ]
机构
[1] UNIV ALBERTA,DEPT PHYS,EDMONTON T6G 2J1,ALBERTA,CANADA
来源
PHYSICAL REVIEW D | 1994年 / 49卷 / 06期
关键词
D O I
10.1103/PhysRevD.49.2872
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly invariant under reparametrizations of the spatial coordinates (''gauge invariant''). At each order we solve the Hamiltonian constraint using a conformal transformation of the three-metric as well as a line integral in superspace. This gives a recursion relation for the generating functional which then may be solved to arbitrary order simply by functionally differentiating previous orders. At fourth order in spatial gradients we demonstrate solutions for irrotational dust as well as for a scalar field. We explicitly evolve the three-metric to the same order. This method can be used to derive the Zel'dovich approximation for general relativity.
引用
收藏
页码:2872 / 2881
页数:10
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