Quantum Effects in General Relativity: Investigating Repulsive Gravity of Black Holes at Large Distances

This paper proposes a theoretical study that investigates quantum effects on the gravity of black holes. This study utilizes a gravitational model that incorporates quantum mechanics derived from the classical-like quantum hydrodynamic representation. This research calculates the mass density distribution of quantum black holes, specifically in the case of central symmetry. The gravity of a quantum black hole shows contributions coming from quantum potential energy, which is also sensitive to the presence of a background of gravitational noise. The additional energy, stored in quantum potential fluctuations and constituting a form of dark energy, leads to a repulsive gravity in the weak gravity limit. This repulsive gravity overcomes the attractive classical Newtonian force at large distances of order of the intergalactic length.