Quasi-Hyperbolically Symmetric γ-Metric

We carry out a systematic study on the motion of test particles in the region inner to the naked singularity of a quasi-hyperbolically symmetric [Formula: see text]-metric. The geodesic equations are written and analyzed in detail. The obtained results are contrasted with the corresponding results obtained for the axially symmetric [Formula: see text]-metric and the hyperbolically symmetric black hole. As in this latter case, it is found that test particles experience a repulsive force within the horizon (naked singularity), which prevents them from reaching the center. However, in the present case, this behavior is affected by the parameter [Formula: see text] which measures the departure from the hyperbolical symmetry. These results are obtained for radially moving particles as well as for particles moving in the [Formula: see text] subspace. The possible relevance of these results in the explanation of extragalactic jets is revealed.