Riemann normal coordinates, smooth lattices and numerical relativity
Riemann normal coordinates, smooth lattices and numerical relativity
复制标题
黎曼法线坐标、光滑晶格和数值相对论
DOI：
10.1088/0264-9381/15/10/014
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发表时间：
1997
影响因子：
3.5
通讯作者：
Leo Brewin
中科院分区：
文献类型：
--
作者：
Leo Brewin
提出了一种新的基于格子的数值相对论方法。该方案使用的数据与Regge演算中使用的数据相同(例如，单纯格子上的一组腿长度)，但它在计算场方程的方式上有很大的不同。在新的方法中，标准的爱因斯坦场方程直接应用于晶格。这是通过使用局部定义的Riemann法线坐标在晶格的局部单元组上插值光滑度量来完成的。将给出Schwarzschild时空的时间对称初始数据的结果。结果表明，该格式对度规和曲率产生了二阶精确的估计(在格子间距中)。它还将表明，比安奇恒等式在Schwarzschild初始数据的构建中发挥着重要作用。
A new lattice-based scheme for numerical relativity will be presented. The scheme uses the same data as would be used in the Regge calculus (e.g. a set of leg lengths on a simplicial lattice), but it differs significantly in the way that the field equations are computed. In the new method the standard Einstein field equations are applied directly to the lattice. This is done by using locally defined Riemann normal coordinates to interpolate a smooth metric over local groups of cells of the lattice. Results for the time-symmetric initial data for the Schwarzschild spacetime will be presented. It will be shown that the scheme yields second-order accurate estimates (in the lattice spacing) for the metric and the curvature. It will also be shown that the Bianchi identities play an essential role in the construction of the Schwarzschild initial data.