Abstract
We first discuss the thermodynamics of a Born-Infeld (BI) black hole enclosed in a finite spherical cavity. A canonical ensemble is considered, which means that the temperature and the charge on the wall of the cavity are fixed. After the free energy is obtained by computing the Euclidean action, it shows that the first law of thermodynamics is satisfied at the locally stationary points of the free energy. The phase structure and transition in various regions of the parameter space are then investigated. In the region where the BI electrodynamics has weak nonlinearities, Hawking-Page-like and van der Waals-like phase transitions occur, and a tricritical point appears. In the region where the BI electrodynamics has strong enough nonlinearities, only Hawking-Page-like phase transitions occur. The phase diagram of a BI black hole in a cavity can have dissimilarity from that of a BI black hole using asymptotically anti-de Sitter boundary conditions. The dissimilarity may stem from a lack of an appropriate reference state with the same charge and temperature for the BI-AdS black hole.
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References
S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-de Sitter Space, Commun. Math. Phys.87 (1983) 577 [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett.B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys.2 (1998) 253 [hep-th/9802150] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys.2 (1998) 505 [hep-th/9803131] [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev.D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Holography, thermodynamics and fluctuations of charged AdS black holes, Phys. Rev.D 60 (1999) 104026 [hep-th/9904197] [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].
R.-G. Cai, Gauss-Bonnet black holes in AdS spaces, Phys. Rev.D 65 (2002) 084014 [hep-th/0109133] [INSPIRE].
D. Kubiznak and R.B. Mann, P-V criticality of charged AdS black holes, JHEP07 (2012) 033 [arXiv:1205.0559] [INSPIRE].
J.W. York Jr., Black hole thermodynamics and the Euclidean Einstein action, Phys. Rev.D 33 (1986) 2092 [INSPIRE].
H.W. Braden, J.D. Brown, B.F. Whiting and J.W. York Jr., Charged black hole in a grand canonical ensemble, Phys. Rev.D 42 (1990) 3376 [INSPIRE].
S. Carlip and S. Vaidya, Phase transitions and critical behavior for charged black holes, Class. Quant. Grav.20 (2003) 3827 [gr-qc/0306054] [INSPIRE].
A.P. Lundgren, Charged black hole in a canonical ensemble, Phys. Rev.D 77 (2008) 044014 [gr-qc/0612119] [INSPIRE].
J.X. Lu, S. Roy and Z. Xiao, Phase transitions and critical behavior of black branes in canonical ensemble, JHEP01 (2011) 133 [arXiv:1010.2068] [INSPIRE].
C. Wu, Z. Xiao and J. Xu, Bubbles and Black Branes in Grand Canonical Ensemble, Phys. Rev.D 85 (2012) 044009 [arXiv:1108.1347] [INSPIRE].
J.X. Lu, R. Wei and J. Xu, The phase structure of black D1/D5 (F/NS5) system in canonical ensemble, JHEP12 (2012) 012 [arXiv:1210.0708] [INSPIRE].
J.X. Lu and R. Wei, Modulating the phase structure of black D6 branes in canonical ensemble, JHEP04 (2013) 100 [arXiv:1301.1780] [INSPIRE].
D. Zhou and Z. Xiao, Phase structures of the black Dp-D(p + 4)-brane system in various ensembles I: thermal stability, JHEP07 (2015) 134 [arXiv:1502.00261] [INSPIRE].
Z. Xiao and D. Zhou, Phase structures of the black Dp-D(p + 4)-brane system in various ensembles II: electrical and thermodynamic stability, JHEP09 (2015) 028 [arXiv:1507.02088] [INSPIRE].
P. Basu, C. Krishnan and P.N. Bala Subramanian, Hairy Black Holes in a Box, JHEP11 (2016) 041 [arXiv:1609.01208] [INSPIRE].
Y. Peng, B. Wang and Y. Liu, On the thermodynamics of the black hole and hairy black hole transitions in the asymptotically flat spacetime with a box, Eur. Phys. J.C 78 (2018) 176 [arXiv:1708.01411] [INSPIRE].
Y. Peng, Studies of a general flat space/boson star transition model in a box through a language similar to holographic superconductors, JHEP07 (2017) 042 [arXiv:1705.08694] [INSPIRE].
Y. Peng, Scalar field configurations supported by charged compact reflecting stars in a curved spacetime, Phys. Lett.B 780 (2018) 144 [arXiv:1801.02495] [INSPIRE].
N. Sanchis-Gual, J.C. Degollado, P.J. Montero, J.A. Font and C. Herdeiro, Explosion and Final State of an Unstable Reissner-Nordström Black Hole, Phys. Rev. Lett.116 (2016) 141101 [arXiv:1512.05358] [INSPIRE].
S.R. Dolan, S. Ponglertsakul and E. Winstanley, Stability of black holes in Einstein-charged scalar field theory in a cavity, Phys. Rev.D 92 (2015) 124047 [arXiv:1507.02156] [INSPIRE].
S. Ponglertsakul, E. Winstanley and S.R. Dolan, Stability of gravitating charged-scalar solitons in a cavity, Phys. Rev.D 94 (2016) 024031 [arXiv:1604.01132] [INSPIRE].
N. Sanchis-Gual, J.C. Degollado, C. Herdeiro, J.A. Font and P.J. Montero, Dynamical formation of a Reissner-Nordström black hole with scalar hair in a cavity, Phys. Rev.D 94 (2016) 044061 [arXiv:1607.06304] [INSPIRE].
S. Ponglertsakul and E. Winstanley, Effect of scalar field mass on gravitating charged scalar solitons and black holes in a cavity, Phys. Lett.B 764 (2017) 87 [arXiv:1610.00135] [INSPIRE].
N. Sanchis-Gual, J.C. Degollado, J.A. Font, C. Herdeiro and E. Radu, Dynamical formation of a hairy black hole in a cavity from the decay of unstable solitons, Class. Quant. Grav.34 (2017) 165001 [arXiv:1611.02441] [INSPIRE].
O.J.C. Dias and R. Masachs, Charged black hole bombs in a Minkowski cavity, Class. Quant. Grav.35 (2018) 184001 [arXiv:1801.10176] [INSPIRE].
O.J.C. Dias and R. Masachs, Evading no-hair theorems: hairy black holes in a Minkowski box, Phys. Rev.D 97 (2018) 124030 [arXiv:1802.01603] [INSPIRE].
F. Simovic and R. Mann, Critical Phenomena of Charged de Sitter Black Holes in Cavities, Class. Quant. Grav.36 (2019) 014002 [arXiv:1807.11875] [INSPIRE].
L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with \( T\overline{T} \), JHEP04 (2018) 010 [arXiv:1611.03470] [INSPIRE].
H.H. Soleng, Charged black points in general relativity coupled to the logarithmic U(1) gauge theory, Phys. Rev.D 52 (1995) 6178 [hep-th/9509033] [INSPIRE].
H. Maeda, M. Hassaine and C. Martinez, Lovelock black holes with a nonlinear Maxwell field, Phys. Rev.D 79 (2009) 044012 [arXiv:0812.2038] [INSPIRE].
S.H. Hendi, B. Eslam Panah, S. Panahiyan and A. Sheykhi, Dilatonic BTZ black holes with power-law field, Phys. Lett.B 767 (2017) 214 [arXiv:1703.03403] [INSPIRE].
J. Tao, P. Wang and H. Yang, Testing holographic conjectures of complexity with Born-Infeld black holes, Eur. Phys. J.C 77 (2017) 817 [arXiv:1703.06297] [INSPIRE].
X. Guo, P. Wang and H. Yang, Membrane Paradigm and Holographic DC Conductivity for Nonlinear Electrodynamics, Phys. Rev.D 98 (2018) 026021 [arXiv:1711.03298] [INSPIRE].
B. Mu, P. Wang and H. Yang, Holographic DC Conductivity for a Power-law Maxwell Field, Eur. Phys. J.C 78 (2018) 1005 [arXiv:1711.06569] [INSPIRE].
S.H. Hendi and M.H. Vahidinia, Extended phase space thermodynamics and P-V criticality of black holes with a nonlinear source, Phys. Rev.D 88 (2013) 084045 [arXiv:1212.6128] [INSPIRE].
J.-X. Mo, G.-Q. Li and X.-B. Xu, Effects of power-law Maxwell field on the critical phenomena of higher dimensional dilaton black holes, Phys. Rev.D 93 (2016) 084041 [arXiv:1601.05500] [INSPIRE].
C.H. Nam, Non-linear charged dS black hole and its thermodynamics and phase transitions, Eur. Phys. J.C 78 (2018) 418 [INSPIRE].
M. Dehghani, Thermodynamic properties of dilaton black holes with nonlinear electrodynamics, Phys. Rev.D 98 (2018) 044008 [INSPIRE].
E. Ayon-Beato and A. Garcia, Regular black hole in general relativity coupled to nonlinear electrodynamics, Phys. Rev. Lett.80 (1998) 5056 [gr-qc/9911046] [INSPIRE].
E. Ayon-Beato and A. Garcia, New regular black hole solution from nonlinear electrodynamics, Phys. Lett.B 464 (1999) 25 [hep-th/9911174] [INSPIRE].
K.A. Bronnikov, Regular magnetic black holes and monopoles from nonlinear electrodynamics, Phys. Rev.D 63 (2001) 044005 [gr-qc/0006014] [INSPIRE].
M. Born and L. Infeld, Foundations of the new field theory, Proc. Roy. Soc. Lond.A 144 (1934) 425.
T.K. Dey, Born-Infeld black holes in the presence of a cosmological constant, Phys. Lett.B 595 (2004) 484 [hep-th/0406169] [INSPIRE].
R.-G. Cai, D.-W. Pang and A. Wang, Born-Infeld black holes in (A)dS spaces, Phys. Rev.D 70 (2004) 124034 [hep-th/0410158] [INSPIRE].
S. Fernando and D. Krug, Charged black hole solutions in Einstein-Born-Infeld gravity with a cosmological constant, Gen. Rel. Grav.35 (2003) 129 [hep-th/0306120] [INSPIRE].
S. Fernando, Thermodynamics of Born-Infeld-anti-de Sitter black holes in the grand canonical ensemble, Phys. Rev.D 74 (2006) 104032 [hep-th/0608040] [INSPIRE].
R. Banerjee, S. Ghosh and D. Roychowdhury, New type of phase transition in Reissner Nordström-AdS black hole and its thermodynamic geometry, Phys. Lett.B 696 (2011) 156 [arXiv:1008.2644] [INSPIRE].
R. Banerjee and D. Roychowdhury, Critical phenomena in Born-Infeld AdS black holes, Phys. Rev.D 85 (2012) 044040 [arXiv:1111.0147] [INSPIRE].
A. Lala and D. Roychowdhury, Ehrenfest’s scheme and thermodynamic geometry in Born-Infeld AdS black holes, Phys. Rev.D 86 (2012) 084027 [arXiv:1111.5991] [INSPIRE].
R. Banerjee and D. Roychowdhury, Critical behavior of Born Infeld AdS black holes in higher dimensions, Phys. Rev.D 85 (2012) 104043 [arXiv:1203.0118] [INSPIRE].
M. Azreg-Aïnou, Black hole thermodynamics: No inconsistency via the inclusion of the missing P-V terms, Phys. Rev.D 91 (2015) 064049 [arXiv:1411.2386] [INSPIRE].
S.H. Hendi, B. Eslam Panah and S. Panahiyan, Einstein-Born-Infeld-Massive Gravity: AdS-Black Hole Solutions and their Thermodynamical properties, JHEP11 (2015) 157 [arXiv:1508.01311] [INSPIRE].
M. Kord Zangeneh, A. Dehyadegari, M.R. Mehdizadeh, B. Wang and A. Sheykhi, Thermodynamics, phase transitions and Ruppeiner geometry for Einstein-dilaton-Lifshitz black holes in the presence of Maxwell and Born-Infeld electrodynamics, Eur. Phys. J.C 77 (2017) 423 [arXiv:1610.06352] [INSPIRE].
X.-X. Zeng, X.-M. Liu and L.-F. Li, Phase structure of the Born-Infeld-anti-de Sitter black holes probed by non-local observables, Eur. Phys. J.C 76 (2016) 616 [arXiv:1601.01160] [INSPIRE].
S. Li, H. Lü and H. Wei, Dyonic (A)dS Black Holes in Einstein-Born-Infeld Theory in Diverse Dimensions, JHEP07 (2016) 004 [arXiv:1606.02733] [INSPIRE].
D.-C. Zou, S.-J. Zhang and B. Wang, Critical behavior of Born-Infeld AdS black holes in the extended phase space thermodynamics, Phys. Rev.D 89 (2014) 044002 [arXiv:1311.7299] [INSPIRE].
S. Hossein Hendi, B. Eslam Panah, S. Panahiyan and M. Hassaine, BTZ dilatonic black holes coupled to Maxwell and Born-Infeld electrodynamics, Phys. Rev.D 98 (2018) 084006 [arXiv:1712.04328] [INSPIRE].
S.H. Hendi and M. Momennia, Reentrant phase transition of Born-Infeld-dilaton black holes, Eur. Phys. J.C 78 (2018) 800 [arXiv:1709.09039] [INSPIRE].
B.R. Majhi and S. Samanta, P-V criticality of AdS black holes in a general framework, Phys. Lett.B 773 (2017) 203 [arXiv:1609.06224] [INSPIRE].
K. Bhattacharya and B.R. Majhi, Thermogeometric description of the van der Waals like phase transition in AdS black holes, Phys. Rev.D 95 (2017) 104024 [arXiv:1702.07174] [INSPIRE].
K. Bhattacharya, B.R. Majhi and S. Samanta, Van der Waals criticality in AdS black holes: a phenomenological study, Phys. Rev.D 96 (2017) 084037 [arXiv:1709.02650] [INSPIRE].
S. Gunasekaran, R.B. Mann and D. Kubiznak, Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization, JHEP11 (2012) 110 [arXiv:1208.6251] [INSPIRE].
A. Dehyadegari and A. Sheykhi, Reentrant phase transition of Born-Infeld-AdS black holes, Phys. Rev.D 98 (2018) 024011 [arXiv:1711.01151] [INSPIRE].
P. Wang, H. Wu and H. Yang, Thermodynamics and Phase Transitions of Nonlinear Electrodynamics Black Holes in an Extended Phase Space, JCAP04 (2019) 052 [arXiv:1808.04506] [INSPIRE].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys.208 (1999) 413 [hep-th/9902121] [INSPIRE].
R. Emparan, C.V. Johnson and R.C. Myers, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev.D 60 (1999) 104001 [hep-th/9903238] [INSPIRE].
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Wang, P., Wu, H. & Yang, H. Thermodynamics and phase transition of a nonlinear electrodynamics black hole in a cavity. J. High Energ. Phys. 2019, 2 (2019). https://doi.org/10.1007/JHEP07(2019)002
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DOI: https://doi.org/10.1007/JHEP07(2019)002