Reference Frames and Black Hole Thermodynamics

TL;DR

This paper explores the relationship between torsion-based boundary terms and black hole thermodynamics within the teleparallel formulation of General Relativity, emphasizing the importance of frame choice for correct entropy and energy calculations.

Contribution

It demonstrates that the connection between torsion boundary terms and black hole entropy depends on the tetrad frame, and identifies specific frames that yield correct thermodynamic quantities without background subtraction.

Findings

Identifies frames where torsion boundary terms match Gibbons-Hawking-York term.

Shows these frames produce correct black hole entropy without background subtraction.

Provides consistent energy calculations from teleparallel energy-momentum pseudo-current.

Abstract

In the context of the absolute parallelism formulation of General Relativity, and because of the fact that the scalar curvature can be written in purely torsional terms, it was known for a long time that a surface term based solely on the torsion tensor appears in the action. It was subsequently suggested that this term might play the role of the Gibbons-Hawking-York boundary term which, in turn, is associated to the free energy in the path integral approach, and then, to the black hole entropy by standard thermodynamic arguments. We show that the identification of the two boundary terms is rather incomplete, and that it strongly depends on the choice of the tetrad (frame) field used to reproduce a given metric. By considering variations of the tetrad field not necessarily subjected to Dirichlet-like conditions on the boundary surface, we find a class of frames adapted to the Schwarzschild spacetime in which the Gibbons-Hawking-York/torsion link is actually established, and conducing to the right black hole entropy without the need of any background subtraction. Remarkably, these frames are also responsible for the correct value of the gravitational energy as computed from the teleparallel energy-momentum pseudo-current.