Non-existence of Singularities in BlackHoles

The foreseeing of singularities within black holes creates a contradiction in modern physics. General relativity argues that at the center of black holes there is curvature and a divergence leading to an incompleteness of space-time. Yet, singularities, on the other hand, are said to not exist in reality due to quantum corrections and models of alternative gravity. In this paper, we provide a proof of singularities nonexistence in a thorough mathematical form based on geodesic completeness, modified Einstein equations, and singularities of quantum gravity.