Abstract
We examine the conjecture that black holes violating the reverse isoperimetric inequality have negative specific heat at constant volume CV [1]. We test this conjecture on the family of generalized exotic Bañados, Teitelboim and Zanelli (BTZ) black holes and find that CV can be positive even when the reverse isoperimetric inequality is violated, providing a counter example to the conjecture. However in all cases where CV is positive, the specific heat at constant pressure CP is negative, indicating that generalized exotic black holes are thermodynamically unstable, suggesting that a broader version of the conjecture might hold.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C.V. Johnson, Instability of Super-Entropic Black Holes in Extended Thermodynamics, arXiv:1906.00993 [INSPIRE].
D. Kubizňák, R.B. Mann and M. Teo, Black hole chemistry: thermodynamics with Lambda, Class. Quant. Grav. 34 (2017) 063001 [arXiv:1608.06147] [INSPIRE].
M. Cvetǐc, G.W. Gibbons, D. Kubizňák and C.N. Pope, Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume, Phys. Rev. D 84 (2011) 024037 [arXiv:1012.2888] [INSPIRE].
B.P. Dolan, The cosmological constant and the black hole equation of state, Class. Quant. Grav. 28 (2011) 125020 [arXiv:1008.5023] [INSPIRE].
D. Kastor, S. Ray and J. Traschen, Enthalpy and the Mechanics of AdS Black Holes, Class. Quant. Grav. 26 (2009) 195011 [arXiv:0904.2765] [INSPIRE].
M.M. Caldarelli, G. Cognola and D. Klemm, Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories, Class. Quant. Grav. 17 (2000) 399 [hep-th/9908022] [INSPIRE].
S. Mbarek and R.B. Mann, Thermodynamic Volume of Cosmological Solitons, Phys. Lett. B 765 (2017) 352 [arXiv:1611.01131] [INSPIRE].
R.A. Hennigar, D. Kubizňák and R.B. Mann, Entropy Inequality Violations from Ultraspinning Black Holes, Phys. Rev. Lett. 115 (2015) 031101 [arXiv:1411.4309] [INSPIRE].
D. Klemm, Four-dimensional black holes with unusual horizons, Phys. Rev. D 89 (2014) 084007 [arXiv:1401.3107] [INSPIRE].
R.A. Hennigar, D. Kubizňák, R.B. Mann and N. Musoke, Ultraspinning limits and super-entropic black holes, JHEP 06 (2015) 096 [arXiv:1504.07529] [INSPIRE].
W.G. Brenna, R.B. Mann and M. Park, Mass and Thermodynamic Volume in Lifshitz Spacetimes, Phys. Rev. D 92 (2015) 044015 [arXiv:1505.06331] [INSPIRE].
S.M. Noorbakhsh and M. Ghominejad, Ultra-Spinning Gauged Supergravity Black Holes and their Kerr/CFT Correspondence, Phys. Rev. D 95 (2017) 046002 [arXiv:1611.02324] [INSPIRE].
S.M. Noorbakhsh and M. Ghominejad, Higher Dimensional Charged AdS Black Holes at Ultra-spinning Limit and Their 2d CFT Duals, arXiv:1702.03448 [INSPIRE].
X.-H. Feng, H.-S. Liu, W.-T. Lu and H. Lü, Horndeski Gravity and the Violation of Reverse Isoperimetric Inequality, Eur. Phys. J. C 77 (2017) 790 [arXiv:1705.08970] [INSPIRE].
S.M. Noorbakhsh and M.H. Vahidinia, Extremal Vanishing Horizon Kerr-AdS Black Holes at Ultraspinning Limit, JHEP 01 (2018) 042 [arXiv:1708.08654] [INSPIRE].
R.B. Mann, Super-Entropic Black Holes, Springer Proc. Phys. 208 (2018) 105 [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
C.V. Johnson, Specific Heats and Schottky Peaks for Black Holes in Extended Thermodynamics, arXiv:1905.00539 [INSPIRE].
A.M. Frassino, R.B. Mann and J.R. Mureika, Extended Thermodynamics and Complexity in Gravitational Chern-Simons Theory, arXiv:1906.07190 [INSPIRE].
A.M. Frassino, R.B. Mann and J.R. Mureika, Lower-Dimensional Black Hole Chemistry, Phys. Rev. D 92 (2015) 124069 [arXiv:1509.05481] [INSPIRE].
E. Witten, (2 + 1)-Dimensional Gravity as an Exactly Soluble System, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
P.K. Townsend and B. Zhang, Thermodynamics of “Exotic” Bañados-Teitelboim-Zanelli Black Holes, Phys. Rev. Lett. 110 (2013) 241302 [arXiv:1302.3874] [INSPIRE].
O. Mǐskovíc and R. Olea, Background-independent charges in Topologically Massive Gravity, JHEP 12 (2009) 046 [arXiv:0909.2275] [INSPIRE].
S. Carlip, J. Gegenberg and R.B. Mann, Black holes in three-dimensional topological gravity, Phys. Rev. D 51 (1995) 6854 [gr-qc/9410021] [INSPIRE].
S. Carlip and J. Gegenberg, Gravitating topological matter in (2 + 1)-dimensions, Phys. Rev. D 44 (1991) 424 [INSPIRE].
M. Bañados, Constant curvature black holes, Phys. Rev. D 57 (1998) 1068 [gr-qc/9703040] [INSPIRE].
M. Bañados, A. Gomberoff and C. Martínez, Anti-de Sitter space and black holes, Class. Quant. Grav. 15 (1998) 3575 [hep-th/9805087] [INSPIRE].
S.N. Solodukhin, Holography with gravitational Chern-Simons, Phys. Rev. D 74 (2006) 024015 [hep-th/0509148] [INSPIRE].
D. Kubizňák and R.B. Mann, P − V criticality of charged AdS black holes, JHEP 07 (2012) 033 [arXiv:1205.0559] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1908.01254
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Cong, W., Mann, R.B. Thermodynamic instabilities of generalized exotic BTZ black holes. J. High Energ. Phys. 2019, 4 (2019). https://doi.org/10.1007/JHEP11(2019)004
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2019)004