Dymnikova Black Hole Tidal Forces

Abstract

In this work we investigate the tidal properties of the Dymnikova regular black hole and their ef fects on massive particles in radial free-fall. Starting from Dymnikova static, spherically symmetric solution, we derive the equations governing timelike radial geodesics and construct an orthonormal tetrad adapted to a free-falling observer. We then obtain the radial and angular components of the tidal tensor and analyze their dependence on the black hole mass and the characteristic length scale of the de Sitter core. At large radial distances, tidal forces recover Schwarzschild behavior, whereas near the regular center, both components remain finite, reflecting the non-singular nature of the spacetime. We show that the radial and angular tidal forces vanish and change sign at characteris tic radii inside the event horizon, indicating transitions between stretching and compression regimes. A particle released from rest outside the event horizon reaches a turnaround point located inside the Cauchy horizon, rather than reaching the regular center. We also solve the geodesic deviation equations for two sets of initial conditions and examine the evolution of the radial and transverse components of the deviation vector. Although the solutions asymptotically reproduce Schwarzschild behavior, they differ significantly in the inner region: the deviation vector components remain finite up to the turnaround point, whereas the corresponding radial component in the Schwarzschild case diverges at the singularity. These results demonstrate how the de Sitter core regularizes the tidal dynamics of extended falling bodies.