The Euclidean path integral approach to quantum gravity is conventionally formulated in terms of the Einstein-Hilbert-York-Gibbons-Hawking action, which requires suitable subtractions to produce the correct black hole partition function. However, there is a unique, canonical teleparallel reformulation which reproduces the same results without subtractions or other ambiguities. This is verified in the case of a black hole with or without an electric or a magnetic charge and in a background with or without a cosmological constant. Moreover, a new quasilocal prescription is proposed and tested, where the black hole partition function is determined solely by the horizon boundary term, yielding the correct Helmholtz free energy without counterterms.

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• General relativity formalism
• Quantum aspects of black holes