Quantum Gravity in Einstein's Theory of General Relativity

The aim of this paper is to show that there are a number of exact solutions in general relativity theory capable of clarifying the compatibility between Einstein's gravitation and quantum mechanics. In this investigation, we rely on two fundamental aspects: In the first aspect we use the fluctuations "noise" of spacetime when the gravitational field is regular in the zone under consideration to show the quantization of gravity and the existence of gravitons. The second aspect is based on the ER=EPR equation formulated by Maldacena and Susskind, which makes it possible to envisage the unification of these theories in the special case of black holes. Using these aspects, we introduce a new equation in the form (ER)1937 = (EPR)1935 capable of highlighting phenomena such as gravitational waves and Hawking radiation ("nuts and bolts" and "wormhole"), which constitute the divergence debate between these two theories. In this formulation, we consider two intricate black holes that form a pair of $EPR$, allowing spacetime to move two regions of space closer together or further apart.