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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.
Yukio Tomozawa (Thu,) studied this question.