Reference frames and black hole thermodynamics

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 sug...

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Bibliographic Details
Published in:Journal of cosmology and astroparticle physics 2023-12, Vol.2023 (12), p.33
Main Authors: Fiorini, Franco, González, P.A., Vásquez, Yerko
Format: Article
Language:English
Subjects:
Black holes
black holes and black hole thermodynamics in GR and beyond
Dirichlet problem
Entropy
Exact solutions
Free energy
GR black holes
Mathematical analysis
modified gravity
Relativity
Tensors
Thermodynamics
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Summary: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.
ISSN:1475-7516
1475-7516
DOI:10.1088/1475-7516/2023/12/033