Quantum Geometrization of Spacetime in General Relativity - Chiarelli, Piero (Quantum Geometrization of Spacetime in General Relativity, 2023)
The primary aim of this study is to establish a unified criterion for obtaining the gravity developed by quantum mass densities within spacetime. This is achieved by extending the principle of equivalence between inertial and gravitational mass, a fundamental aspect of General Relativity, to the covariance of equations of motion. In the classical scenario, we obtain the gravity of spacetime with classical characteristics, whereas in the quantum scenario, we obtain the gravity of spacetime with quantum mechanical properties. In both cases, the principle of least action is employed to define the geometry of spacetime. The gravity resulting from the quantum geometrization of spacetime can be seen as the quantum mechanical counterpart of General Relativity, where the fields of quantum physics are integrated into the theory of gravitation. In this study, we derive the gravity generated by boson and fermion fields. The outcomes of the theory have been utilized to derive antimatter gravity, resolve black hole singularities, and understand the origin of small-valued cosmological constants. The work also derives the fluctuations of the black hole quantum potential in the presence of the gravitational wave background and evaluates the resultant repulsive gravity at large distances. Furthermore, it examines the breaking of the matter-antimatter symmetry caused by the gravitational coupling of the fermions field. The significance of matter-antimatter asymmetry in pre-big bang black hole is described: This behavior implies that the matter-antimatter asymmetry might have played a crucial role in the highly energetic vacuum states of the pre-big bang black hole. When surpassing the Planck mass, the high-energy fermion state in the pre-big bang black hole's comprised fermion and antifermion black holes. The annihilation of these black holes emitted lighter fermions, accounting for the mass difference between the black hole and anti-black hole. The theory shows that as we approach the Minkowskian limit, the matter-antimatter symmetry becomes asymptotically established, and the mass disparity between particles and antiparticles diminishes as we transition from heavier to lighter particles within each particle family. The theory also shows that if the matter-antimatter symmetry were upheld, the vacuum would have collapsed into the polymer branched phase because there would have been no residual mass (resulting from the matter-antimatter difference) to stabilize the vacuum and confer a nonzero cosmological constant. Thus, the matter-antimatter symmetry in a quantum mechanical covariant gravity is incongruent with the formation of a physically stable vacuum with non-zero mean cosmological constant value. The process of quantum geometrization of spacetime provides a comprehensive framework for understanding the evolution of our universe, from the Pre-big bang black hole to the current quantum-decoherent classical reality. The theory posits that the ubiquitous presence of supermassive black holes (SMBHs) at the centers of galaxies is a direct consequence of the big-bang, from which SMBHs are generated without mass accretion, and that it plays a pivotal role in cosmological expansion, driven by their repulsive interactions. Finally, the system of field equations for Quantum Electrodynamics (QED) in curved spacetime (containing the fields back-reaction), along with an introductory section on the Standard Model in self-generated gravity is presented. The problem of second quantization of fields in spacetime with the coupled gravity of is also introduced. This has the potential to extend the standard Quantum Field Theory (QFT) to high energies. Experimental tests examining the disparities in magnetic moments between leptons and antileptons, as well as investigations involving entangled photons, are proposed as potential avenues for empirically validating the theory.