-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.Introduction. -Nearly 100 years ago, on the Russian front, Karl Schwarzschild found the first exact solutions to the Einstein field equations, a few weeks after the publication of the general theory of relativity (and a few months before dying). These solutions describe the geometry of empty spacetime around an uncharged, spherically-symmetric, and non-rotating body [1]. The generalization to a charged source was found soon after [2,3]. However, it took almost fifty years to discover the exact solutions for a rotating, axially-symmetric object, which were found by Kerr in 1963 [4]. As usual, the extension to the charged case, i.e. the Kerr-Newman solution, followed shortly thereafter [5]. Further contributions to the investigation of the Kerr metric came in several papers in the following years (e.g. [6][7][8][9][10][11]). In particular, efforts were spent to understand the complete topology of Kerr spacetime.A peculiar aspect of this topology, which was not present in the static Schwarzschild case and in its analytic extensions (e.g. [12][13][14][15]), is the existence of the negative-r region, i.e. the r coordinate is no longer conditioned by the usual restriction r ≥ 0, but is allowed to take also negative values, as a Cartesian coordinate. To a physicist this freedom may appear rather embarrassing, also because it is not easy to explain what sense may have this 'doubling' of space of which he had never felt the need before. Here we investigate the properties of this unknown region and seek to give a physical interpretation.