Quantum corrections to gravity

TL;DR

This paper investigates quantum corrections to gravity, demonstrating that such corrections can make gravity repulsive at short distances, and confirms the exact solutions for spherically symmetric metrics.

Contribution

It shows that the Gauss-Bonnet combination is the correct quantum correction in curved spacetime and confirms an exact solution for a spherically symmetric static metric.

Findings

Quantum corrections introduce quadratic curvature terms in gravity.

Only the Gauss-Bonnet combination yields correct quantum corrections.

Gravity becomes repulsive at short distances due to quantum effects.

Abstract

This paper revisits quantum corrections to gravity. It was shown previously by other authors that quantum field theories in curved space time provide quadratic curvature forms as quantum corrections to gravity in a conformally flat metric. Application to a spherically symmetric and static (SSS) metric shows that only the Gauss Bonnet combination (GB) yields the correct expression. Using a variational method, the author shows that the metric he obtained in 1985 as an example in a simplified case was indeed the exact solution for a SSS metric. This proves that gravity becomes repulsive at short distances by quantum corrections.