Black hole thermodynamics and boundary terms in teleparallel gravity

Teleparallel equivalent of General Relativity is an alternative theory of gravity that describes gravitational interactions only in terms of spacetime torsion instead of curvature. This theory can also be nicely formulated as a gauge theory for the translation group. TEGR is believed to be equivalent to General Relativity since their corresponding actions are equal up to a boundary term B. However, boundary terms do affect black hole thermodynamics. So, one could expect to obtain different results concerning BH thermodynamics in TEGR. However, at least at the leading order, this turns out not to be the case. Indeed, in this work we compute entropy and energy of the Teleparallel equivalent of a Schwarzschild BH, and we find that these values agree with those obtained in GR. Also, we construct the TEGR analog of the Landau-Lifshitz energy-momentum pseudo-tensor, from which we obtain the total conserved energy of Teleparallel Schwarzschild BH. This allows us to confirm the previous results, reinforcing the equivalence of black hole thermodynamics in GR and TEGR at the leading order. Upon quantization, however, higher-order terms are expected to show up and spoil this equivalence. Thus, we study as well one-loop corrections to the partition function. To this purpose, we employed heat kernel methods to calculate the one-loop divergences of the effective action of a scalar field minimally coupled to gravity in TEGR. We find that these divergences are the same as what one obtains in GR. Then, we give some hints on the analogous calculations for the gravitational sector of the theory. In particular, we find out the second-order differential operator relevant for the heat kernel method and we present a simple argument that seems to indicate that the one-loop divergences of quantum TEGR are the same as in quantum GR too. However, there is a possible shortcoming concerning 1-loop corrections since the needed counterterms are not expected to have all the symmetries of TEGR.