Expert: James Gort - 9/2/2007

Question
When a massive rotating star collapses to a black hole why isn't the rotational angular velocity of the black hole infinite?  If a black hole is a singularity with zero diameter the conservation of angular momentum should result in infinite rational velocity.


Answer
Hi Paul,

When a rotating star collapses, you are correct that conservation of angular momentum (which is another way of saying conservation of rotational energy) must be obeyed.  However, relativity also has its say!  And that says the maximum angular momentum which a black hole can have is G * M^2 / c.  If the angular momentum exceeds that, the black hole can't exist.  As far as we can tell, nature doesn't allow that to happen.  So what happens to that excess angular momentum?  Well, before the matter crosses the event horizon, the excess angular momentum (remember, it's rotational energy) is radiated away, primarily as gravitational waves.  

But what happens it a black hole exists, rotating at or near its maximum, and another star or black hole (say, with spin in the same direction) tries to enter it?  Well, the curved spacetime which actually accelerates bodies into the black hole plays a different role here.  A spin-spin force is induced which is just strong enough to keep the rotating body from entering the event horizon!  You can say it's black hole repulsion!

Of course, a body rotating in the opposite direction could easily enter the event horizon, since the sum of the angular momenta means the total would be reduced.

BTW, a rotating black hole produces a ring singularity rather than a point singularity.

Hope that helps!

Prof. James Gort