Topological origin of horizon temperature via the Chern–Gauss–Bonnet theorem

封面

如何引用文章

全文:

开放存取 开放存取
受限制的访问 ##reader.subscriptionAccessGranted##
受限制的访问 订阅或者付费存取

详细

This paper establishes a connection between the Hawking temperature of spacetime horizons and global topological invariants, specifically the Euler characteristic of Wick-rotated Euclidean spacetimes. This is demonstrated for both de Sitter and Schwarzschild, where the compactification of the near-horizon geometry allows for a direct application of the Chern–Gauss–Bonnet theorem. For de Sitter, a simple argument connects the Gibbon–Hawking temperature of the Bunch–Davies state to the global thermal de Sitter temperature. This establishes that spacetime thermodynamics are a consequence of the geometrical structure of spacetime itself, therefore suggesting a deep connection between global topology and semi-classical analysis.

作者简介

J. Hughes

College of Engineering and Physical Sciences, Khalifa University

Email: jack.hughes.phys.14@gmail.com
Abu Dhabi, United Arab Emirates

F. Kusmartsev

College of Engineering and Physical Sciences, Khalifa University

Email: fedor.kusmartsev@ku.ac.ae
Abu Dhabi, United Arab Emirates

参考

  1. G.W. Gibbons and S.W. Hawking, Phys. Rev. D 15, 2752 (1977); URL https://journals.aps.org/prd/abstract/10.1103/PhysRevD.15.2752.
  2. G.W. Gibbons and S.W. Hawking, Phys. Rev. D 15, 2738 (1977).
  3. G.E. Volovik, Symmetry 16, 763 (2024); Preprint 2312.02292[gr-qc].
  4. G.E. Volovik, arXiv:2504.05763 [gr-qc]; Preprint 2504.05763[gr-qc] (2025).
  5. S. Carlip, Int. J. Mod. Phys. D 23, 1430023 (2014); Preprint 1410.1486[gr-qc].
  6. A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, Rev. Mod. Phys. 93, 035002 (2021); URL https://arxiv.org/abs/2006.06872.
  7. D. Diakonov, arXiv:2504.01942 [hep-th]; Preprint 2504.01942[hep-th] (2025).
  8. B.S. Kay and R.M. Wald, Phys. Rep. 207, 49 (1991).
  9. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).
  10. P.C. Martin and J.S. Schwinger, Phys. Rev. 115, 1342 (1959).
  11. N.D. Birrell and P.C.W. Davies, Quantum fields in curved space, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, UK (1982); ISBN 978-0521278584.
  12. T. Padmanabhan, Rep. Prog. Phys. 73, 046901 (2010); Preprint 0911.5004.
  13. E.W. Mielke, Geometrodynamics of Gauge Fields: On the Geometry of Yang-Mills and Gravitational Gauge Theories, Mathematical Physics Studies, 2nd ed., Springer, Cham (2017); ISBN 978-3-319-29733-0.
  14. L.W. Tu, Differential Geometry: Connections, Curvature, and Characteristic Classes, Graduate Texts in Mathematics, Springer, Cham, Switzerland (2017), v. 275; ISBN 978-3-319-55082-4.
  15. J.C.M. Hughes and F.V. Kusmartsev, arXiv:2403.11527 [gr-qc]; Preprint 2403.11527[gr-qc] (2024).
  16. S.S. Chern, Ann. Math. 45, 747 (1944).
  17. S.S. Chern, Ann. Math. 46, 674 (1945).
  18. J.C.M. Hughes and F.V. Kusmartsev, arXiv:2505.05814 [gr-qc]; Preprint 2505.05814 (2025).
  19. G.E. Volovik, arXiv:2505.20194; Preprint 2505.20194 (2025).
  20. G.E. Volovik, JETP Lett. 90, 1 (2009); Preprint 0905.4639 [gr-qc].
  21. A. Hatcher, Algebraic Topology, Cambridge University Press, Cambridge (2001); ISBN 9780521795401.

补充文件

附件文件
动作
1. JATS XML
下载

版权所有 © Russian Academy of Sciences, 2025