General Solutions to the Linearized Einstein Equations and Initial Data for Three Dimensional Time Evolution of Pure Gravitational Waves
General Solutions to the Linearized Einstein Equations and Initial Data for Three Dimensional Time Evolution of Pure Gravitational Waves
复制标题
纯引力波三维时间演化的线性爱因斯坦方程和初始数据的通解
DOI：
10.1143/ptp.72.746
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发表时间：
1984
影响因子：
--
通讯作者：
Takashi Nakamura
中科院分区：
文献类型：
--
作者：
Takashi Nakamura
给出了爱因斯坦方程[3+ 1]-形式下线性化引力波在恒移函数和零移矢量规范条件下的通解。利用上述通解，给出了纯引力波三维时间演化的初始数据。三维空间是保形不变的。对动量约束方程进行了解析求解。采用离散球谐法对哈密顿约束方程进行了数值求解。对于初始数据的时间演化，给出了球极坐标系中度量张量在任何时刻都应满足的正则性条件。
General solutions to the linearized gravitational waves under the gauge condition of constant lapse function and zero shift vector in the [3+ l]-formalism of the Einstein equations are given. Using the above general solution, we give the initial data of the three dimensional time evolution of pure gravitational waves. The three dimensional space is conformally fiat. The momentum constraint equations are solved analytically. The Hamiltonian constraint equation is solved numerically by using discrete spherical harmonics. As for the time evolution of the initial data, we give regularity conditions which metric tensors in the spherical polar coordinates should satisfy at any time.