Characterizing repulsive gravity with curvature eigenvalues

Understand

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.