Characterizing repulsive gravity with curvature eigenvalues
  Repulsive gravity has been investigated in several scenarios near compact
objects by using different intuitive approaches. Here, we propose an invariant
method to characterize regions of repulsive gravity, associated to black holes
and naked singularities. Our method is based upon the behavior of the curvature
tensor eigenvalues, and leads to an invariant definition of a \emph{repulsion
radius}. The repulsion radius determines a physical region, which can be
interpreted as a repulsion sphere, where the effects due to repulsive gravity
naturally arise. Further, we show that the use of effective masses to
characterize repulsive regions can lead to coordinate-dependent results
whereas, in our approach, repulsion emerges as a consequence of the spacetime
geometry in a completely invariant way. Our definition is tested in the
spacetime of an electrically charged Kerr naked singularity and in all its
limiting cases. We show that a positive mass can generate repulsive gravity if
it is equipped with an electric charge or an angular momentum. We obtain
reasonable results for the spacetime regions contained inside the repulsion
sphere whose size and shape depend on the value of the mass, charge and angular
momentum. Consequently, we define repulsive gravity as a classical relativistic
effect by using the geometry of spacetime only.
