Euclidean teleparallel relativity and black hole partition functions

TL;DR

The paper addresses the need for boundary subtractions in Euclidean quantum gravity within GR and proposes a canonical teleparallel reformulation, G_parallel_R, that yields the same black hole thermodynamics without counterterms. By working in an inertial frame, the bulk action vanishes and the partition function is controlled by boundary terms, with a quasilocal horizon prescription enabling the Helmholtz free energy to be read off directly from horizon data. The authors demonstrate, across Schwarzschild, charged, de Sitter, and anti-de Sitter cases, that the resulting partition functions reproduce expected thermodynamics without ad hoc adjustments, and in AdS they clarify the role of a finite-radius cutoff in obtaining a canonical partition function. The framework suggests improved UV behavior and potential renormalisability for Euclidean quantum gravity in the teleparallel setting, and motivates further study beyond on-shell configurations and in more general spacetimes.

Abstract

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.