# What happens if I were to add angular momentum to a maximally spinning black hole? [duplicate]

I am aware that a "naked singularity" is not possible. However, what would happen if I added angular momentum to a black hole near the maximal angular momentum limit? Does it asymptote?

• Can you add angular momentum without adding more mass? – Rob Jeffries Apr 21 at 7:13

The equations you have to look at are on wikipedia see especially this section. One way of expressing the limit is given there as $$GM^2 < Jc$$ where $$J$$ is the angular momentum. Suppose you have a black hole just under this limit and add an object of mass $$m$$ angular momentum just under $$Gm^2/c$$ velocoty just under $$c$$ and on a trajectory that just grazes the Schwarzchild radius of the hole at $$\frac{2GM}{c^2}$$. The angular moment of the result is just under $$GM^2/c + 2GMmc/c^2 + Gm^2/c$$ where the terms are respectively the original angular moment of the hole, the angular moment from the grazing impact and the angular momentum of the added body. This works out to be (just under) $$G(M+m)^2/c$$, the limit for the (now-enlarged) black hole.