Euclidean teleparallel relativity and black hole partition functions

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 the need for counterterms.