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It has been known for many years that the leading correction to the blackhole entropy is a logarithmic term, which is universal and closely related toconformal anomaly. A fully consistent analysis of this issue has to takequantum backreactions to the black hole geometry into account. However, it wasalways unclear how to naturally derive the modified black hole metricespecially from an effective action, because the problem refers to the elusivenon-locality of quantum gravity. In this paper, we show that this problem canbe resolved within an effective field theory (EFT) framework of quantumgravity. Our work suggests that the EFT approach provides a powerful andself-consistent tool for studying the quantum gravitational corrections toblack hole geometries and thermodynamics.

Logarithmic correction to black hole entropy from the nonlocality of quantum gravity