Euclidean black holes and spin connection

  • P. Valtancoli Dipartimento di Fisica, Polo Scientifico Universitá di Firenze, 50019 Sesto Fiorentino, Italy; INFN, Sezione di Firenze, 50019 Sesto Fiorentino, Italy
Article ID: 652
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Keywords: black holes; Wick rotation; spin connection; general relativity; thermodynamics

Abstract

The Euclidean method is usually discussed in the context of the metric avoiding the typical delta of the conical singularity. We introduce a new way to calculate the Hawking temperature using the vierbein and spin connection. The conical singularity is seen globally through an effect on parallel transport, the so called holonomy of the spin connection. The period of the Euclidean time is calculated requiring that the holonomy of the spin connection is trivial at the event horizon.

Published
2024-12-05
Section
Original Research Articles

References

Gibbons GW, Hawking SW. Action integrals and partition functions in quantum gravity. Phys. Rev. D. 1977; 15: 2752.

Wald RW. General Relativity. The University of Chicago Press; 1984.

York JW. Black-hole thermodynamics and the Euclidean Einstein action. Phys. Rev. D. 1986; 33: 2092.

Mann RB, Solodukhin SN. Conical singularity and quantum corrections to the entropy of a black hole. Phys. Rev. D. 1996; 54: 3932.

Morvan EK, van der Schaar JP, Visser MR. On the Euclidean Action of de Sitter Black Holes and Constrained Instantons. Sci. Post. Phys. 2023; 14: 022.

’t Hooft G. On the Quantum Structure of a Black Hole. Nucl. Phys. B. 1985; 256: 727.

Demers JG, Lafrance R, Myers RC. Black hole entropy without brick walls. Phys. Rev. D. 1995; 52: 2245.

Visser M. Feynman’s i-epsilon prescription, almost real spacetimes, and acceptable complex spacetimes. Journal of High Energy Physics. 2022; 08: 129. arXiv: 2111.14016v3 [gr-qc]

Samuel J. Wick Rotation in the Tangent Space. Classical and Quantum GravityClassical and Quantum Gravity. 2016; 33: 015006. arXiv: 1510. 07365v1 [gr qc]