Geometric origin of a stable black hole remnant from torsion in G$$_2$$-manifold geometry

Abstract In this work, we explore the phenomenological consequences of a 7-dimensional Einstein-Cartan theory formulated on a G $$_2$$ 2 -manifold with torsion. We demonstrate that a Kaluza-Klein reduction of this geometry can provide a natural origin for the electroweak scale ( $$\approx \thickapprox {246}{GeV}$$ ≈ ≈ 246 GeV ), offering a geometric explanation for the hierarchy problem. A key prediction of this framework is the existence of a repulsive force at Planckian densities, which dynamically halts the final stage of Hawking evaporation. This leads to the formation of a stable remnant with a predicted mass of approximately $$9\times 10^{-41}\;\text {kg}$$ 9 × 10 - 41 kg . The model’s internal consistency is confirmed by non-trivial relations that fix its geometric parameters, leading to falsifiable predictions. Furthermore, the remnant’s structure provides a concrete mechanism for storing information via its quasi-normal mode spectrum, opening a new, testable research program at the intersection of geometry, quantum gravity, and particle physics.