Abstract
The first law of black hole mechanics, which relates the change of energy to the change of entropy and other conserved charges, has been the main motivation for probing the thermodynamic properties of black holes. In this work, we investigate the thermodynamics of Kerr Taub-NUT AdS black holes. We present geometric Komar definitions for the black hole charges, that by construction satisfy the Smarr formula. Further, by a scaling argument based on Euler’s theorem, we establish the first law for the Kerr Taub-NUT AdS black holes. The corresponding first law includes variations in the cosmological constant, NUT charges and angular momenta. The key new ingredient in the construction are the independent variations of both angular momenta, the black hole and Misner string angular momenta. Employing the Brown-York quasi-local charge definitions we show that our expression for the mass and spin coincide with our generalized Komar expressions. We indicate the relevance of these results to the thermodynamics of rotating AdS black holes, including the proper choice of time-like Killing vector to produce the correct thermodynamic mass.
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References
R.B. Mann, Entropy of rotating Misner string space-times, Phys. Rev. D 61 (2000) 084013 [hep-th/9904148] [INSPIRE].
D. Astefanesei, R.B. Mann and E. Radu, Nut charged space-times and closed timelike curves on the boundary, JHEP 01 (2005) 049 [hep-th/0407110] [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].
R.A. Hennigar, D. Kubizňák and R.B. Mann, Thermodynamics of Lorentzian Taub-NUT spacetimes, Phys. Rev. D 100 (2019) 064055 [arXiv:1903.08668] [INSPIRE].
A.B. Bordo, F. Gray and D. Kubizňák, Thermodynamics and phase transitions of NUTty dyons, JHEP 07 (2019) 119 [arXiv:1904.00030] [INSPIRE].
R. Clarkson, L. Fatibene and R.B. Mann, Thermodynamics of (d + 1)-dimensional NUT charged AdS space-times, Nucl. Phys. B 652 (2003) 348 [hep-th/0210280] [INSPIRE].
R. Clarkson, A.M. Ghezelbash and R.B. Mann, Mass, action and entropy of Taub-Bolt-dS space-times, Phys. Rev. Lett. 91 (2003) 061301 [hep-th/0304097] [INSPIRE].
T. Padmanabhan, Some aspects of field equations in generalised theories of gravity, Phys. Rev. D 84 (2011) 124041 [arXiv:1109.3846] [INSPIRE].
C.V. Johnson, Thermodynamic volumes for AdS-Taub-NUT and AdS-Taub-Bolt, Class. Quant. Grav. 31 (2014) 235003 [arXiv:1405.5941] [INSPIRE].
G. Clément, D. Gal’tsov and M. Guenouche, Rehabilitating space-times with NUTs, Phys. Lett. B 750 (2015) 591 [arXiv:1508.07622] [INSPIRE].
R. Araneda, R. Aros, O. Mišković and R. Olea, Magnetic mass in 4D AdS gravity, Phys. Rev. D 93 (2016) 084022 [arXiv:1602.07975] [INSPIRE].
L. Donnay and G. Giribet, Cosmological horizons, Noether charges and entropy, Class. Quant. Grav. 36 (2019) 165005 [arXiv:1903.09271] [INSPIRE].
U. Kol and M. Porrati, Properties of dual supertranslation charges in asymptotically flat spacetimes, Phys. Rev. D 100 (2019) 046019 [arXiv:1907.00990] [INSPIRE].
R. Durka, The first law of black hole thermodynamics for Taub-NUT spacetime, Int. J. Mod. Phys. D 31 (2022) 2250021 [arXiv:1908.04238] [INSPIRE].
L. Ciambelli, C. Corral, J. Figueroa, G. Giribet and R. Olea, Topological terms and the Misner string entropy, Phys. Rev. D 103 (2021) 024052 [arXiv:2011.11044] [INSPIRE].
A. Ballon Bordo, F. Gray, R.A. Hennigar and D. Kubizňák, The first law for rotating NUTs, Phys. Lett. B 798 (2019) 134972 [arXiv:1905.06350] [INSPIRE].
G.W. Gibbons, M.J. Perry and C.N. Pope, The first law of thermodynamics for Kerr-anti-de Sitter black holes, Class. Quant. Grav. 22 (2005) 1503 [hep-th/0408217] [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.W. Hawking, C.J. Hunter and M. Taylor, Rotation and the AdS/CFT correspondence, Phys. Rev. D 59 (1999) 064005 [hep-th/9811056] [INSPIRE].
A.B. Bordo, F. Gray, R.A. Hennigar and D. Kubizňák, Misner gravitational charges and variable string strengths, Class. Quant. Grav. 36 (2019) 194001 [arXiv:1905.03785] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [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].
M. Sharif and Q. Ama-Tul-Mughani, Effects of thermal fluctuations on the Kerr-Newman-NUT-AdS black hole, Commun. Theor. Phys. 73 (2021) 085402.
J.B. Griffiths and J. Podolsky, A new look at the Plebanski-Demianski family of solutions, Int. J. Mod. Phys. D 15 (2006) 335 [gr-qc/0511091] [INSPIRE].
V.A. Kostelecky and M.J. Perry, Solitonic black holes in gauged N = 2 supergravity, Phys. Lett. B 371 (1996) 191 [hep-th/9512222] [INSPIRE].
C.W. Misner, The flatter regions of Newman, Unti and Tamburino’s generalized Schwarzschild space, J. Math. Phys. 4 (1963) 924 [INSPIRE].
D. Kubiznak and P. Krtous, On conformal Killing-Yano tensors for Plebanski-Demianski family of solutions, Phys. Rev. D 76 (2007) 084036 [arXiv:0707.0409] [INSPIRE].
M. Cvetič, G.W. Gibbons, D. Kubiznak 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].
J.D. Brown and J.W. York, Jr., Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D 47 (1993) 1407 [gr-qc/9209012] [INSPIRE].
W. Chen, H. Lü and C.N. Pope, General Kerr-NUT-AdS metrics in all dimensions, Class. Quant. Grav. 23 (2006) 5323 [hep-th/0604125] [INSPIRE].
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Rodríguez, N.H., Rodriguez, M.J. First law for Kerr Taub-NUT AdS black holes. J. High Energ. Phys. 2022, 44 (2022). https://doi.org/10.1007/JHEP10(2022)044
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DOI: https://doi.org/10.1007/JHEP10(2022)044