Separability of the massive Dirac's equation in 5-dimensional Myers-Perry black hole geometry and its relation to a rank-three Killing-Yano tensor

Understand

The Dirac equation for the electron around a five-dimensional rotating black hole with two different angular momenta is separated into purely radial and purely angular equations.

• The general solution is expressed as a superposition of solutions derived from these two decoupled ordinary differential equations.
• By separating variables for the massive Klein-Gordon equation in the same space-time background, I derive a simple and elegant form for the Stackel-Killing tensor, which can be easily written as the square of a rank-three Killing-Yano tensor.
• I have also explicitly constructed a symmetry operator that commutes with the scalar Laplacian by using the Stackel-Killing tensor, and the one with the Dirac operator by the Killing-Yano tensor admitted by the five-dimensional Myers-Perry metric, respectively.