论文标题
Bowen-York模型解决方案REDUX
Bowen-York Model Solution Redux
论文作者
论文摘要
常规相对论中的初始值问题通常是数值解决的。只有少数例外，其中一个是Bowen和York的“模型”解决方案，其中可以使用该解决方案的分析形式。该解决方案描述了具有质量和线性动量的动力学，时空引力系统。在这里，我们重新访问该解决方案并纠正错误，该误差对于识别解决方案的能量符号很重要。根据线性动量，初始能量的非平稳部分与总ADM能量的比率为$ [0，0.592）$的值。在系统的演变过程中，预计该非平稳部分将变成重力波，以使可能沉降到具有质量和线性动量的黑洞。在超友善的情况下（高动量极限），重力波能量的最大量为$ 59.2 \％$的总能量。我们还详细说明了哈密顿约束的一般解决方案。
Initial value problem in General Relativity is often solved numerically; with only a few exceptions one of which is the "model" solution of Bowen and York where an analytical form of the solution is available. The solution describes a dynamical, time-asymmetric, gravitating system with mass and linear momentum. Here we revisit this solution and correct an error which turns out to be important for identifying the energy-content of the solution. Depending on the linear momentum, the ratio of the non-stationary part of the initial energy to the total ADM energy takes values between $[0, 0.592)$. This non-stationary part is expected to be turned into gravitational waves during the evolution of the system to possibly settle down to a black hole with mass and linear momentum. In the ultra-relativistic case (the high momentum limit), the maximum amount of gravitational wave energy is $59.2 \%$ of the total ADM energy. We also give a detailed account of the general solution of the Hamiltonian constraint.
