Duerr, Detlef; Struyve, Ward
(2020):
Quantum Einstein equations.
In: Classical and Quantum Gravity, Vol. 37, No. 13, 135002

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Abstract
We derive the quantum Einstein equations (which are the quantum generalisation of the Einstein equations of classical gravity) from Bohmian quantum gravity. Bohmian quantum gravity is a nonclassical geometrodynamics (in the ADM formalism) which describes the time evolution of a threegeometry and of a matter field (or other matter degrees of freedom) on a three manifold. The evolution is determined by a velocity law which is defined by the wave function. The wave function itself satisfies the WheelerDeWitt equation. We cast the Bohmian dynamics into the form of the Einstein field equations, where the interesting novelty is a contribution to the energymomentum tensor that depends on the quantum potential.