Quantum Effects in General Relativity: [...] Repulsive Gravity of Black Holes at Large Distances

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This work shows that quantum black holes with a central symmetry have a mass density distribution that is not point-like but is concentrated in a sphere with a radius in the order of its Compton wavelength. Due to significant quantum potential energy, there exists a supplemental term in the gravity equation, resulting in an additional contribution to the gravity force at large dis-tances. The pressure density tensor is a function of mass fields and demonstrates a point-specific behavior akin to the quintessence model. However, what sets it apart is its reliance on the quantum properties of space–time instead of an elusive physical field. The present model shows that the alteration of Newtonian gravity over long distanc-es is explained by the gravitational effect of the quantum potential of enormously massive entities, such as black holes and supermassive black holes, subject to background dark energy fluctuations. In the presence of fluctuations in the space–time background metric, the dark energy arising from fluctuations in the quantum potential energy of black holes results in a repulsive contribution to gravitational force. , mediated by the pressure-density tensor. This repulsive force of SMBH dominates over the Newtonian force at distances characteristic of intergalactic space. On this basis, it has the capacity to generate a cosmo-logical constant producing the acceleration of the universe, aligning reasonably well with the observed low value. Furthermore, the establishment of a minimum radius for the mass distribution of black holes, which solves the issue of classical general relativity’s point singularity, and subsequently, the determination of a minimum mass required for black hole formation, represents the foremost large-scale manifestation of quantum effects on the curvature of spacetime as posited by the theory. This concept holds important significance as it en-sures the stability of our universe, preventing elementary particles from spontaneously generating black holes and averting the excessive production of microscopic black holes due to quantum vacuum instability.

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