Myers-Perry black hole

A Myers-Perry black hole is the higher-dimensional asymptotically flat rotating vacuum generalization of the Kerr black hole. In six dimensions, a solution with one nonzero rotation parameter $a$ and horizon radius $r_{+}$ has mass parameter $\mu =r_{+}(r_{+}^2+a^2)$.

A five-dimensional Myers-Perry black hole with equal rotational parameters has a metric depending on a single radial coordinate. In a fibered coordinate system, its radial functions can be written $f=1-r_0^2/r^2+{\alpha }^2{r}_0^2/r^4$, $h=1+{\alpha }^2{r}_0^2/r^4$, and $\Omega =\alpha r_0^2/(r^{4}h)$. For $0<\alpha <r_0/2$ there are outer and inner Killing horizons; at equality they form a degenerate Killing horizon. With the standard sphere identifications and $G_5=1$, its Komar mass is $3\pi r_0^2/8$.

For the singly rotating six-dimensional Myers-Perry solution with $G=1$ and $\mu =r_{+}(r_{+}^2+a^2)$,and the horizon area is