Collapsing stars and coriolis force

If you ice skater pulls in his/her arms, she will spin faster. This is because of conservation of angular momentum. However there are two interesting things that are usually not said:

Her rotational kinetic energy is not conserved, it will go up since E = \frac{1}{2} I \omega ^2

The energy comes from doing work from pulling her arms inside against the centrifugal/inertial forces of her arms.

However the centrifugal force cannot increase her angular velocity since it is radially outward and perpendicular. The coriolis force actually increases the speed.

Since large stars collapsing is kind of similar to the ice skater I wonder how this process goes. Angular momentum needs to be conserved, however I have the feeling that inertial forces in GR act strange and I wonder if there is still a perfect balance. How does the centrifugal force change in a highly rotating massive system and the coriolis effect. Are there any other interesting things going on during the collapse?