Gabriel horn (G-horn) with finite volume but infinite surface area can characterize the frame-dragging effects of strong gravitational fields. Subject to the gravitational bounce depending on velocity direction, a G-horn black hole model is established on the Finsler geometric framework. Beyond considering curvature alone, the torsion determined by Cartan connection gives rise to Coriolis force and centrifugal force to counteract gravitational collapse. The G-horn topological structure determines the property that the mathematical singularity and the center of matter converging region need not coincide. Without hidden or naked singularities, the matter after entering this black hole is choked at a certain inner-surface zone of horn’s neck to form a regular “hollow” core based on spin-flip trigger of Cartan torsion. During geodesic fluctuations in the G-horn model, the existence of black hole remnants is rigorously derived. Due to the global geodesic completeness, those existing paradoxes or hypotheses such as black hole information loss, Penrose's cosmic censorship and firewalls are just the competition results between gravity of curvature and the resultant inertial forces of “centrifugal force ± Coriolis force” of torsion. The proposed G-horn map implies that the Schwarzschild, Kerr and Reissner‑Nordström black holes may be modified uniformly as this hyperbolic G-horn model.