I have been experimenting with different types of metric tensors in General Relativity. I decided to try my hand with the Kerr Metric. When I did, I found an odd term in it: namely, a cross product of $dt$ and $d\phi$. My question is, why sort of physical meaning does this cross product have? What does it mean?
Here is the full Kerr Metric for reference:\begin{aligned}c^{2}d\tau ^{2}=&\left(1-{\frac {r_{s}r}{\rho ^{2}}}\right)c^{2}dt^{2}-{\frac {\rho ^{2}}{\Delta }}dr^{2}-\rho ^{2}d\theta ^{2}\\&-\left(r^{2}+\alpha ^{2}+{\frac {r_{s}r\alpha ^{2}}{\rho ^{2}}}\sin ^{2}\theta \right)\sin ^{2}\theta \ d\phi ^{2}+{\frac {2r_{s}r\alpha \sin ^{2}\theta }{\rho ^{2}}}\,c\,dt\,d\phi \end{aligned} $r_{s}$ is the Schwarzschild Radius, $r,\theta,\phi$ are the standard spherical coordinate system, and where $\alpha,\rho,\Delta$ have been introduced for brevity. $${\displaystyle \rho ^{2}=r^{2}+\alpha ^{2}\cos ^{2}\theta }$$ $${\displaystyle \alpha ={\frac {J}{Mc}}}$$ $${\displaystyle \Delta =r^{2}-r_{s}r+\alpha ^{2}}$$