Black hole critical behavior with the generalized BSSN formulation
Black hole critical behavior with the generalized BSSN formulation
复制标题
广义 BSSN 公式的黑洞临界行为
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
M. Choptuik
中科院分区：
文献类型：
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作者：
A. Akbarian;M. Choptuik
爱因斯坦方程的双曲公式的发展彻底改变了我们对强场引力现象进行长期、稳定、精确的数值模拟的能力。然而，双曲方法在II型临界崩溃领域的应用相对较少，其中数值代码的挑战特别严重。以球对称下无质量标量场的临界坍缩为例，研究了适合于曲线坐标的基于Brown的Baumgarte-Shapiro-Shibata-Nakamura公式的推广。我们采用标准的动态测量选择，包括1+对数切片和零或由伽马驱动条件演变的移位。通过这两种位移选择，我们都能够进化到足够接近黑洞阈值，从而(1)明确地识别临界解的离散自相似性，(2)确定与先前计算一致的回声指数，以及(3)测量质量缩放指数，也与先前的计算一致。我们的结果可以被视为在更一般的II型情景中使用双曲公式的令人鼓舞的第一步，包括尚未解决的轴对称引力波的临界坍缩问题。
The development of hyperbolic formulations of Einstein's equations has revolutionized our ability to perform long-time, stable, accurate numerical simulations of strong field gravitational phenomena. However, hyperbolic methods have seen relatively little application in one area of interest, type II critical collapse, where the challenges for a numerical code are particularly severe. Using the critical collapse of a massless scalar field in spherical symmetry as a test case, we study a generalization of the Baumgarte-Shapiro-Shibata-Nakamura formulation due to Brown that is suited for use with curvilinear coordinates. We adopt standard dynamical gauge choices, including 1+log slicing and a shift that is either zero or evolved by a Gamma-driver condition. With both choices of shift we are able to evolve sufficiently close to the black hole threshold to (1) unambiguously identify the discrete self-similarity of the critical solution, (2) determine an echoing exponent consistent with previous calculations, and (3) measure a mass scaling exponent, also in accord with prior computations. Our results can be viewed as an encouraging first step towards the use of hyperbolic formulations in more generic type II scenarios, including the as yet unresolved problem of critical collapse of axisymmetric gravitational waves.