标题： 计算极限曲面上准局部自旋和其他不变量的新方法 显示英文标题

标题： A new method to compute quasi-local spin and other invariants on marginally trapped surfaces

摘要： 我们准确计算了数值3+1模拟中极限陷阱面上的标量2曲率、Weyl标量、相关的准局部自旋、质量以及高阶多极矩。 为了确定准局部量，我们引入了一种新方法，该方法需要一组不变的表面积分，仅需几百个点的表面网格即可。 新方法避免了解Killing方程，并且也是近似Killing向量场的替代方法。 我们将该方法应用于一个扰动的非轴对称黑洞，使其衰减为Kerr黑洞，并将准局部自旋与其他使用Killing向量场、坐标向量场、准正则振荡和Kerr度规在表面上的性质的方法进行比较。 有趣的是，在扰动轴对称阶段，与近似Killing向量场的自旋一致。 此外，我们引入了一种新的坐标变换，将球坐标适配到球面上的任意两点，如轴对称陷阱面上标量2曲率的两个最小值。 显示英文摘要

摘要： We accurately compute the scalar 2-curvature, the Weyl scalars, associated quasi-local spin, mass and higher multipole moments on marginally trapped surfaces in numerical 3+1 simulations. To determine the quasi-local quantities we introduce a new method which requires a set of invariant surface integrals, allowing for surface grids of a few hundred points only. The new technique circumvents solving the Killing equation and is also an alternative to approximate Killing vector fields. We apply the method to a perturbed non-axisymmetric black hole ringing down to Kerr and compare the quasi-local spin with other methods that use Killing vector fields, coordinate vector fields, quasinormal ringing and properties of the Kerr metric on the surface. Interesting is the agreement with the spin of approximate Killing vector fields during the phase of perturbed axisymmetry. Additionally, we introduce a new coordinate transformation, adapting spherical coordinates to any two points on the sphere like the two minima of the scalar 2-curvature on axisymmetric trapped surfaces.