CTTK: a new method to solve the initial data constraints in numerical relativity
CTTK: a new method to solve the initial data constraints in numerical relativity
复制标题
CTTK：解决数值相对论中初始数据约束的新方法
DOI：
10.1088/1361-6382/acb883
复制
发表时间：
2023
影响因子：
3.5
通讯作者：
Aurrekoetxea J
中科院分区：
文献类型：
--
作者：
Aurrekoetxea J
在具有非平凡物质组态的数值相对论模拟中，必须求解初始数据中度规变量的ADM公式的哈密顿约束和动量约束。我们介绍了一种基于标准共形横向无迹分解的新方案，在该方案中，不是将哈密顿约束作为二阶椭圆型方程来求解平均曲率K的选择，而是求解K的代数方程来选择保形因子。通过这样做，我们避免了哈密顿约束解的存在唯一性问题，而不使用通常的源项的共形重新标度。当震源是基本场时，这一点尤其重要，因为根据重新标度的量来重构场的配置可能会有问题。利用迭代多重网格求解器，我们证明了该方法对数值相对论中尚未研究的几个初始条件提供了快速收敛的解，即(A)具有大的随机高斯标量场扰动的周期性非均匀时空和(B)具有旋转标量云的渐近平坦的黑洞时空。
In numerical relativity simulations with non-trivial matter configurations, one must solve the Hamiltonian and momentum constraints of the ADM formulation for the metric variables in the initial data. We introduce a new scheme based on the standard conformal transverse-traceless decomposition, in which instead of solving the Hamiltonian constraint as a 2nd order elliptic equation for a choice of mean curvature K, we solve an algebraic equation for K for a choice of conformal factor. By doing so, we evade the existence and uniqueness problem of solutions of the Hamiltonian constraint without using the usual conformal rescaling of the source terms. This is particularly important when the sources are fundamental fields, as reconstructing the fields' configurations from the rescaled quantities is potentially problematic. Using an iterative multigrid solver, we show that this method provides rapid convergent solutions for several initial conditions that have not yet been studied in numerical relativity; namely (a) periodic inhomogeneous spacetimes with large random Gaussian scalar field perturbations and (b) asymptotically flat black hole spacetimes with rotating scalar clouds.