# Particle falling into a Kerr black hole

Let's say that a particle starts a radial free fall towards a Kerr black hole with zero initial energy at $$r\rightarrow\infty$$. The initial angular momentum of the particle is zero ($$p_\phi = 0)$$. From the Kerr metric, $$p_\phi$$ and $$E$$ are the constants of motion for the particle geodesic. However, we know that inside the ergosphere, we have a frame dragging effect, which means that the particle will start rotating after it enters into the ergosphere. Does it mean that inside the ergosphere, the particle angular momentum $$p_\phi$$ is nonzero and $$p_\phi$$ is not a constant of motion anymore?

• relative to the local ZAMOs the tangential velocity of the infalling particle remains 0 all the way. If the axial angular momentum Lz=0, the particle always corotates with the local frame dragging velocity, and therefore vφ=0 in the local ZAMO's frame. It is like in this animation, but time reversed: yukterez.net/org/kerr.orbits/kerresc3.html Dec 13 '19 at 0:58