- Letter
- Open Access
Thermodynamics in spacetimes without horizons
Phys. Rev. D 112, L101502 – Published 5 November, 2025
DOI: https://doi.org/10.1103/zzg7-vjb8
Abstract
We consider the energetics and thermodynamics of spacetimes with no horizons, but endowed with a preferred timelike junction surface. They could arise as a limiting case of the gravastar and other constructions regularizing the interior of the horizon of a black hole, or from the conceptual cutting of a portion of a nonasymptotically flat space and gluing it with flat space. We find that such surfaces can be made to have zero energy, so that the energetics of such spaces is not encumbered by them. They do have a transverse pressure, fixed by the jump in surface gravity. A peculiar matter thermodynamics then follows, with well-defined entropy, temperature, and surface pressure, constrained by specific relations arising from the zero energy condition. This is confirmed by the Euclidean path integral, with the proviso that the Tolman-Ehrenfest temperature should be used. The entropy of the space is then the area of the timelike surface in units of a fundamental area, and the matter temperature is proportional to the transverse pressure and so the jump in surface gravity. However, when the gravitational action is added, the free energy of the surface is also zero. The fact that for some such spaces the temperature comes out negative raises interesting questions regarding the third “law” of thermodynamics.
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References (20)
- J. D. Bekenstein, Lett. Nuovo Cimento 4, 737 (1972).
- J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973).
- J. D. Bekenstein, Phys. Rev. D 9, 3292 (1974).
- J. M. Bardeen, B. Carter, and S. W. Hawking, Commun. Math. Phys. 31, 161 (1973).
- G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2738 (1977).
- P. O. Mazur and E. Mottola, Proc. Natl. Acad. Sci. U.S.A. 101, 9545 (2004).
- P. O. Mazur and E. Mottola, Universe 9, 88 (2023).
- R. C. Tolman, Phys. Rev. 35, 904 (1930); R. C. Tolman and P. Ehrenfest, 36, 1791 (1930).
- J. D. Brown and J. W. York, Jr., arXiv:gr-qc/9405024; Phys. Rev. D 47, 1407 (1993).
- C. Rovelli and M. Smerlak, Classical Quantum Gravity 28, 075007 (2011).
- W. Israel, Nuovo Cimento B 44, 1 (1966); 48, 463(E) (1967).
- E. Poisson, A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics: Hypersurfaces (Cambridge University Press, Cambridge, England, 2004).
- C. W. Misner and D. H. Sharp, Phys. Rev. 136, B571 (1964).
- S. A. Hayward, Classical Quantum Gravity 15, 3147 (1998).
- E. Mottola, Regular Black Holes, Springer Series in Astrophysics and Cosmology: Gravitational Vacuum Condensate Stars (Springer Singapore, 2023).
- C. Misner, K. Thorne, and J. A. Wheeler, Gravitation (Princeton University Press, 2017).
- J. D. Brown, Classical Quantum Gravity 10, 1579 (1993).
- G. Ballesteros, D. Comelli, and L. Pilo, Phys. Rev. D 94, 025034 (2016).
- H. A. Chamblin and H. S. Reall, Nucl. Phys. B562, 133 (1999).
- R. R. Caldwell, A. Chamblin, and G. W. Gibbons, Phys. Rev. D 53, 7103 (1996).
