From General Relativity to Feynman Path Integral: Toward a Penrose-Like Solution for Black Holes and Cyclic Universes

In this paper, we explore a theoretical framework aimed at bridging general relativity and quantum mechanics by employing the Feynman path integral formalism. Starting from Einstein’s field equations, we cautiously propose a transition to quantum behavior with the normalization of covariant derivatives at the Planck scale. Following Richard Feynman’s path integral approach, we extend this formalism into curved spacetime and consider its possible implications for black hole physics. Additionally, we draw on Roger Penrose’s ideas regarding black hole entropy and conformal cyclic cosmology. This model suggests that black holes, rather than representing the final stages of gravitational collapse, might contribute to the formation of new universes, in line with Penrose’s concept of cyclic cosmology. We carefully examine both Schwarzschild and Kerr black holes and suggest that quantum tunneling across event horizons could theoretically permit a transition from black holes to white holes, potentially facilitating cosmological cycles. This approach could offer new insights into the information paradox and contribute, albeit modestly, to the ongoing discourse surrounding the unification of general relativity and quantum mechanics.