Solving parallel transport equations in the higher-dimensional Kerr-NUT-(A)dS spacetimes

Understand

We obtain and study the equations describing the parallel transport of orthonormal frames along geodesics in a spacetime admitting a non-degenerate principal conformal Killing-Yano tensor h.

• We demonstrate that the operator F, obtained by a projection of h to a subspace orthogonal to the velocity, has in a generic case eigenspaces of dimension not greater than 2.
• Each of these eigenspaces are independently parallel-propagated.
• This allows one to reduce the parallel transport equations to a set of the first order ordinary differential equations for the angles of rotation in the 2D eigenspaces.