  Repulsive gravity is not very popular in physics. However, one comes across
it in at least two main occurrences in general relativity: in the negative-$r$
region of Kerr spacetime, and as the result of the gravitational interaction
between matter and antimatter, when the latter is assumed to be CPT-transformed
matter. Here we show how these two independent developments of general
relativity are perfectly consistent in predicting gravitational repulsion and
how the above Kerr negative-$r$ region can be interpreted as the habitat of
antimatter. As a consequence, matter particles traveling along vortical
geodesics can pass through the throat of a rotating black hole and emerge as
antimatter particles (and vice versa). An experimental definitive answer on the
gravitational behavior of antimatter is awaited in the next few years.
