# Massless Kerr black hole

It's simply flat space in Boyer-Lindquist coordinates. By writing

$$\begin{cases} x=\sqrt{r^2+a^2}\sin\theta\cos\phi\\ y=\sqrt{r^2+a^2}\sin\theta\sin\phi\\ z=r\cos\theta \end{cases}$$

you'll get good ol' $$\mathbb{M}^4$$.

This is presumably a flat spacetime described in funny coordinates. You can check this by calculating the Riemann tensor to see if it's zero. If I was going to do this, I would code it in the open-source computer algebra system Maxima, using the ctensor package.

A reference which answers this is Visser (2008). It discusses the limits of vanishing mass $$M \rightarrow 0$$, and rotation parameter $$a \rightarrow 0$$. Your example is in $$\S5$$. Visser comments "This is flat Minkowski space in so-called “oblate spheroidal” coordinates...", as described in a different answer here.