The Lazarus project: A pragmatic approach to binary black hole evolutions
The Lazarus project: A pragmatic approach to binary black hole evolutions
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拉撒路项目：双黑洞演化的实用方法
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
C. Lousto
中科院分区：
文献类型：
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作者：
John G. Baker;John G. Baker;M. Campanelli;M. Campanelli;C. Lousto;C. Lousto;C. Lousto
我们详细描述了结合 3D 数值模拟和随后的单个黑洞近极限近似而开发的技术。该方法使得计算涵盖双黑洞系统后轨道动力学的第一个完整波形成为可能，并在接近极限适用于后期动力学之前通过数值模拟涵盖基本的非线性相互作用。为了将完整的数值方法和微扰方法结合起来，我们必须解决几个问题。为了确定何时适用近极限扰动理论，我们应用不变先验估计和后验一致性检查的组合来检查结果的鲁棒性，以防止界面附近线性和非线性处理的交换。我们的方法始于标准数值技术的专门应用，以适应当前简短但准确的模拟的现实目标。一旦数值模拟的双星系统达到可以被视为克尔时空扰动的状态，我们必须将数值坐标与扰动背景坐标近似关联起来。我们还执行数值定义的四分体的旋转，以渐进地再现微扰处理中所需的四分体。然后，我们可以以 Weyl 标量 c 4 及其时间导数 ] tc 4 的形式生成近极限演化的数值柯西数据，这两个对象都是一阶坐标和四分体不变量。采用Boyer-Lindquist坐标系中的Teukolsky方程进一步继续演化。为了说明这些技术的应用，我们发展了单个克尔孔并计算杂散辐射作为整个过程误差的度量。我们还简要讨论了该项目的扩展，以利用改进的全数值演化，并概述了我们现在可以追求的全面理解天体物理黑洞双星系统的方法。
We present a detailed description of techniques developed to combine 3D numerical simulations and, subsequently, a single black hole close-limit approximation. This method has made it possible to compute the first complete waveforms covering the post-orbital dynamics of a binary‐black-hole system with the numerical simulation covering the essential nonlinear interaction before the close limit becomes applicable for the late time dynamics. In order to couple full numerical and perturbative methods we must address several questions. To determine when close-limit perturbation theory is applicable we apply a combination of invariant a priori estimates and a posteriori consistency checks of the robustness of our results against exchange of linear and nonlinear treatments near the interface. Our method begins with a specialized application of standard numerical techniques adapted to the presently realistic goal of brief, but accurate simulations. Once the numerically modeled binary system reaches a regime that can be treated as perturbations of the Kerr spacetime, we must approximately relate the numerical coordinates to the perturbative background coordinates. We also perform a rotation of a numerically defined tetrad to asymptotically reproduce the tetrad required in the perturbative treatment. We can then produce numerical Cauchy data for the close-limit evolution in the form of the Weyl scalar c 4 and its time derivative ] tc 4 with both objects being first order coordinate and tetrad invariant. The Teukolsky equation in Boyer-Lindquist coordinates is adopted to further continue the evolution. To illustrate the application of these techniques we evolve a single Kerr hole and compute the spurious radiation as a measure of the error of the whole procedure. We also briefly discuss the extension of the project to make use of improved full numerical evolutions and outline the approach to a full understanding of astrophysical black-hole‐binary systems which we can now pursue.