Quasi--hyperbolically symmetric $\gamma$-metric

TL;DR

This paper investigates test particle motion near a quasi-hyperbolically symmetric $b3$-metric's naked singularity, revealing repulsive forces that prevent particles from reaching the center, with potential implications for extragalactic jets.

Contribution

It provides a detailed analysis of geodesics in a quasi-hyperbolic $b3$-metric and compares the effects of the symmetry parameter $b3$ on particle dynamics.

Findings

Particles experience repulsive forces preventing horizon crossing.

The behavior depends on the symmetry parameter $b3$.

Results may explain phenomena like extragalactic jets.

Abstract

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 $\gamma$-metric. The geodesic equations are written and analyzed in detail. The obtained results are contrasted with the corresponding results obtained for the axially symmetric $\gamma$-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 to reach the center. However in the present case this behavior is affected by the parameter $\gamma$ which measures the departure from the hyperbolical symmetry. These results are obtained for radially moving particles as well as for particles moving in the $\theta-r$ subspace. Possible relevance of these results in the explanation of extragalactic jets, is brought out.