Kerr horizon angular velocity (${\Omega }_H=a/(r_{+}^2+a^2)$)

The outer Killing horizon of a Kerr black hole is generated by $k+{\Omega }_{H}m$, with the stationary Killing vector field $k$ normalized at infinity and the axial generator $m$ having $2\pi$-periodic orbits. In ingoing Kerr coordinates its generators satisfy $d\chi /dv={\Omega }_H$. This is the horizon's angular velocity relative to the nonrotating asymptotic stationary frame.