Abstract
We construct a model for considering the quantum correction of the gravitational constant. In the model, the gravitational constant originates from a coupling between the gravitational field and a scalar field. If the scalar field, as it should be in the real physical world, is a quantum field, the gravitational constant will have a quantum correction. The quantum correction, generally speaking, varies with spacetime coordinates. Therefore, the gravitational constant is no longer a constant. In different spacetime, the quantum correction is different, for the coupling in different spacetime is different. As a result, the gravitational constant in different spacetime is different, though the difference is only at the quantum level. We calculate the quantum correction of the gravitational constant in the Schwarzschild spacetime, the H3 (Euclidean AdS3) spacetime, the H3/Z spacetime, the universe model, the de Sitter spacetime, and the Rindler spacetime.
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