分析力学在广义相对论中的应用

The Application of Analytic Mechanics to General Relativity

将分析力学中的Hamilton变分原理运用到广义相对论中,通过构造引力场的Lagrange函数,导出大尺度时空中的引力场所满足的Lagrange运动方程,即Einstein引力场方程.进一步,将四维时空流形进行3+1分解,通过Legendre变换和Dirac约束分析,得到引力场方程的Hamilton形式,即引力场演化方程和约束方程,从而能清晰地展现出引力场所受的约束条件和演化规律.

The Homihonian variational principle is applied into general relativity in this paper. The Lagrange equations of motion satisfied by gravitational field in the large scale spacetime, i.e. , Einstein field equations for gravitation, can be derived by constructing the Lagrange function of gravitational field. Furthermore, the Hamihonian formulation of field equations for gravitation, i. e. , evolution equations and constraint equations for gravitational field, can be also obtained by Legendre transformation and Dirac constraint analysis after the 3 ＋ 1 decomposion of 4 - dimensional spacetime. Hence the constraint conditions and evolution laws satisfied by gravitational field can be evidently shown.