Tetrad formalism for numerical relativity on conformally compactified constant mean curvature hypersurfaces
Tetrad formalism for numerical relativity on conformally compactified constant mean curvature hypersurfaces
复制标题
共形紧致常平均曲率超曲面数值相对论的四分形式
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
L. Buchman
中科院分区：
文献类型：
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作者：
J. Bardeen;O. Sarbach;L. Buchman
我们提出了一个新的爱因斯坦场方程的演化系统，它是基于四元组场和共形紧化的双曲空间超曲面，达到未来的零无穷大。在四分体的选择的助推自由度是固定的，要求其类时的腿是正交的叶理，其中包括恒定的平均曲率片。四分体中的旋转自由度由3D Nester规范固定。在这些条件下，场方程自然地归结为一阶约束对称双曲演化系统，该系统耦合到规范变量的椭圆方程。明确给出了共形重标度方程，并讨论了它们在未来零无穷远处的正则性。我们的公式是潜在的有用的高精度数值模拟的引力辐射的吸入和合并黑洞双星和其他高度相对论性的孤立系统。
We present a new evolution system for Einstein’s field equations which is based on tetrad fields and conformally compactified hyperboloidal spatial hypersurfaces which reach future null infinity. The boost freedom in the choice of the tetrad is fixed by requiring that its timelike leg be orthogonal to the foliation, which consists of constant mean curvature slices. The rotational freedom in the tetrad is fixed by the 3D Nester gauge. With these conditions, the field equations reduce naturally to a first-order constrained symmetric hyperbolic evolution system which is coupled to elliptic equations for the gauge variables. The conformally rescaled equations are given explicitly, and their regularity at future null infinity is discussed. Our formulation is potentially useful for high accuracy numerical modeling of gravitational radiation emitted by inspiraling and merging black hole binaries and other highly relativistic isolated systems.