The matter-antimatter interpretation of Kerr spacetime
  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. 
M. Villata
gr-qc