Reference Frames and Black Hole Thermodynamics

F.FIORINI; P. GONZÁLEZ; Y. VÁSQUEZ

JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS

IOP PUBLISHING LTD

Lugar: Londres; Año: 2023 vol. 12

1475-7516

In the context of the absolute parallelism formulation of General Relativity, andbecause of the fact that the scalar curvature can be written in purely torsional terms, it wasknown for a long time that a surface term based solely on the torsion tensor appears in theaction. It was subsequently suggested that this term might play the role of the GibbonsHawking-York boundary term which, in turn, is associated to the free energy in the pathintegral 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 reproducea given metric. By considering variations of the tetrad field not necessarily subjected toDirichlet-like conditions on the boundary surface, we find a class of frames adapted to theSchwarzschild 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 backgroundsubtraction. Remarkably, these frames are also responsible for the correct value of the gravitational energy as computed from the teleparallel energy-momentum pseudo-current.