Quantum correction of gravitational constant

TL;DR

This paper proposes a model where the gravitational constant is affected by quantum effects of a scalar field, leading to spacetime-dependent variations in the gravitational constant across different spacetime geometries.

Contribution

It introduces a novel approach to quantum corrections of the gravitational constant, showing it varies with spacetime when the scalar field is quantum in nature.

Findings

Quantum correction makes the gravitational constant spacetime-dependent.

Corrections vary across different spacetime geometries.

Explicit calculations in multiple spacetime models.

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 $AdS_{3}$) spacetime, the $H_{3}/Z$ spacetime, the universe model, the de Sitter spacetime, and the Rindler spacetime.