We carry out a systematic study on the motion of test particles in the region inner to the horizon of a hyperbolically symmetric black hole. The geodesic equations are written and analyzed in detail. The obtained results are contrasted with the corresponding results obtained for the spherically symmetric case. It is found that test particles experience a repulsive force within the horizon, which prevents them to reach the center. These results are obtained for radially moving particles as well as for particles moving in the $\theta -R$ subspace. To complement our study we calculate the precession of a gyroscope moving along a circular path (nongeodesic) within the horizon. We obtain that the precession of the gyroscope is retrograde in the rotating frame, unlike the precession close to the horizon ($R=2m+\epsilon$) in the Schwarzschild spacetime, which is forward.

• Received 25 November 2019
• Revised 27 February 2020
• Accepted 13 March 2020

DOI:https://doi.org/10.1103/PhysRevD.101.064071