= Closed timelike circles in negative-radius Kerr spacetime
{title2=$g_{\phi\phi}=r^2+a^2+2Ma^2/r<0\quad(r<0\text{ near }0)$}
On the equatorial plane of the <Kerr metric>, the displayed component is negative for sufficiently small negative $r$. A curve of constant $t,r,\theta=\pi/2$, with $\phi$ increasing through $2\pi$, is therefore a regular <closed timelike curve>. It avoids the ring at $r=0$. Such circles occur on the negative-radius sheet of the exact analytic extension, not in the exterior region accessible from positive-radius infinity.
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