Quantum correction of gravitational constant

Abstract

We suggest a scheme for considering the quantum correction of the gravitational constant. In the model, the gravitational constant originates from a coupling of the gravitational field with a scalar field. In this paper, we show that if the scalar field, as it should be in the real physical world, is a quantum field, then the gravitational constant will have a spacetime-dependent quantum correction, so that the quantum corrected physical constant is no longer a constant. The quantum correction of the gravitational constant is different in different spacetime. We calculate the quantum correction in the Schwarzschild spacetime, the $H_3$ (Euclidean $Ad{S}_3$) spacetime, the $H_3/Z$ spacetime, the universe model, the de Sitter spacetime, and the Rindler spacetime.

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