One-loop Renormalization of Black Hole Entropy Due to Non-minimally Coupled Matter

The quantum entanglement entropy of an eternal black hole is studied. We argue that the relevant Euclidean path integral is taken over fields defined on $α$-fold covering of the black hole instanton. The statement that divergences of the entropy are renormalized by renormalization of gravitational couplings in the effective action is proved for non-minimally coupled scalar matter. The relationship of entanglement and thermodynamical entropies is discussed.

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