The initial value problem as it relates to numerical relativity
The initial value problem as it relates to numerical relativity
复制标题
与数值相对论相关的初值问题
DOI：
10.1088/1361-6633/80/2/026901
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发表时间：
2016
影响因子：
18.1
通讯作者：
W. Tichy
中科院分区：
文献类型：
--
作者：
W. Tichy
在广义相对论的 3+1 分裂中，时空被空间超曲面所分割。初始值问题包括为这样一个空间超曲面上的所有场指定初始数据，以便完全确定随后的时间演化。在每个超曲面上，3 度量曲率和外在曲率描述了几何形状。与流体速度、能量密度和静止质量密度等物质场一起，3 度量曲率和外在曲率构成了初始数据。选择此类初始数据有很大的自由度。这种自由度对应于系统初始时的物理状态。同时初始数据必须满足广义相对论的哈密顿方程和动量约束方程，因此不能完全自由选择。我们讨论了共形横向无痕分解和共形薄夹层分解，它们常用于构造满足初始数据的约束。这些分解使我们能够指定描述系统物理性质的某些自由数据。然后通过求解从约束方程导出的椭圆方程来确定剩余的度量字段。我们描述了单个黑洞和单个中子星的初始数据，以及如何使用共形分解来构造由黑洞或中子星组成的双星的初始数据。绕轨道运行的双星会发射引力辐射，从而损失能量。由于随着时间的推移，发射的辐射倾向于使轨道呈圆形，因此可以预期典型双星中的物体在半径缓慢缩小的几乎圆形的轨道上运动。这引出了准平衡的概念，它本质上假设对于几乎圆形轨道上的双星来说，时间导数在共转坐标中可以忽略不计。我们回顾了如何使用准平衡假设来做出物理上有充分动机的近似，从而简化我们必须求解的椭圆方程。
Spacetime is foliated by spatial hypersurfaces in the 3+1 split of general relativity. The initial value problem then consists of specifying initial data for all fields on one such a spatial hypersurface, such that the subsequent evolution forward in time is fully determined. On each hypersurface the 3-metric and extrinsic curvature describe the geometry. Together with matter fields such as fluid velocity, energy density and rest mass density, the 3-metric and extrinsic curvature then constitute the initial data. There is a lot of freedom in choosing such initial data. This freedom corresponds to the physical state of the system at the initial time. At the same time the initial data have to satisfy the Hamiltonian and momentum constraint equations of general relativity and can thus not be chosen completely freely. We discuss the conformal transverse traceless and conformal thin sandwich decompositions that are commonly used in the construction of constraint satisfying initial data. These decompositions allow us to specify certain free data that describe the physical nature of the system. The remaining metric fields are then determined by solving elliptic equations derived from the constraint equations. We describe initial data for single black holes and single neutron stars, and how we can use conformal decompositions to construct initial data for binaries made up of black holes or neutron stars. Orbiting binaries will emit gravitational radiation and thus lose energy. Since the emitted radiation tends to circularize the orbits over time, one can thus expect that the objects in a typical binary move on almost circular orbits with slowly shrinking radii. This leads us to the concept of quasi-equilibrium, which essentially assumes that time derivatives are negligible in corotating coordinates for binaries on almost circular orbits. We review how quasi-equilibrium assumptions can be used to make physically well motivated approximations that simplify the elliptic equations we have to solve.
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影响因子：
5
作者：
R. Gold;S. Bernuzzi;M. Thierfelder;B. Brügmann;F. Pretorius
通讯作者：
F. Pretorius
影响因子：
5
作者：
N. Moldenhauer;C. M. Markakis;N. K. Johnson-McDaniel;W. Tichy;B. Brügman
通讯作者：
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影响因子：
3.5
作者：
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影响因子：
5
作者：
T. Dietrich;N. Moldenhauer;N. K. Johnson-McDaniel;S. Bernuzzi;C. M. Markakis;B. Brügmann;W. Tichy
通讯作者：
W. Tichy
影响因子：
5
作者：
B. Bruegmann;José A. González;M. Hannam;S. Husa;U. Sperhake;W. Tichy
通讯作者：
B. Bruegmann;José A. González;M. Hannam;S. Husa;U. Sperhake;W. Tichy