Page Don N, Kubiznák David, Vasudevan Muraari, Krtous Pavel
Theoretical Physics Institute, University of Alberta, Edmonton, Alberta, Canada.
Phys Rev Lett. 2007 Feb 9;98(6):061102. doi: 10.1103/PhysRevLett.98.061102.
We explicitly exhibit n-1=[D/2]-1 constants of motion for geodesics in the general D-dimensional Kerr-NUT-AdS rotating black hole spacetime, arising from contractions of even powers of the 2-form obtained by contracting the geodesic velocity with the dual of the contraction of the velocity with the (D-2)-dimensional Killing-Yano tensor. These constants of motion are functionally independent of each other and of the D-n+1 constants of motion that arise from the metric and the D-n=[(D+1)/2] Killing vectors, making a total of D independent constants of motion in all dimensions D. The Poisson brackets of all pairs of these D constants are zero, so geodesic motion in these spacetimes is completely integrable.
我们明确展示了一般(D)维克尔 - 纽特 - 反德西特旋转黑洞时空中测地线的(n - 1 = [D / 2] - 1)个运动常数，这些运动常数源于通过将测地线速度与速度与((D - 2))维基灵 - 矢野张量收缩的对偶收缩得到的(2)形式的偶次幂的收缩。这些运动常数在功能上相互独立，并且与由度规和(D - n = [(D + 1) / 2])个基灵矢量产生的(D - n + 1)个运动常数相互独立，从而在所有维度(D)中总共产生(D)个独立的运动常数。这(D)个常数中任意两个的泊松括号均为零，因此这些时空中的测地线运动是完全可积的。
