Abstract
We extend the work on thermodynamics of Lorentzian NUTty solutions, by including simultaneously the effect of rotation and electromagnetic charges. Due to the fact that Misner strings carry electric charge, and similar to the non-rotating case, we observe an interesting interplay between the horizon and asymptotic charges. Namely, upon employing the Euclidean action calculation we derive two alternative full cohomogeneity first laws, one that includes the variations of the horizon electric charge and the asymptotic magnetic charge and another that involves the horizon magnetic charge and the asymptotic electric charge. When one of the horizon charges vanishes, we obtain the corresponding ‘electric’ and ‘magnetic’ first laws that are connected by the electromagnetic duality. We also briefly study the free energy of the corresponding system.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A.H. Taub, Empty space-times admitting a three parameter group of motions, Annals Math. 53 (1951) 472.
E. Newman, L. Tamburino and T. Unti, Empty space generalization of the Schwarzschild metric, J. Math. Phys. 4 (1963) 915 [INSPIRE].
W.B. Bonnor, A new interpretation of the NUT metric in general relativity, Math. Proc. Cambridge Phil. Soc. 66 (1969) 145.
V.S. Manko and E. Ruiz, Physical interpretation of NUT solution, Class. Quant. Grav. 22 (2005) 3555 [gr-qc/0505001] [INSPIRE].
C.W. Misner, The flatter regions of Newman, Unti and Tamburino’s generalized Schwarzschild space, J. Math. Phys. 4 (1963) 924 [INSPIRE].
D.N. Page, Taub-NUT Instanton With an Horizon, Phys. Lett. 78B (1978) 249 [INSPIRE].
D.N. Page, A compact rotating gravitational instanton, Phys. Lett. 79B (1978) 235 [INSPIRE].
S.W. Hawking and C.J. Hunter, Gravitational entropy and global structure, Phys. Rev. D 59 (1999) 044025 [hep-th/9808085] [INSPIRE].
S.W. Hawking, C.J. Hunter and D.N. Page, Nut charge, anti-de Sitter space and entropy, Phys. Rev. D 59 (1999) 044033 [hep-th/9809035] [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Large N phases, gravitational instantons and the nuts and bolts of AdS holography, Phys. Rev. D 59 (1999) 064010 [hep-th/9808177] [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].
R.B. Mann, Misner string entropy, Phys. Rev. D 60 (1999) 104047 [hep-th/9903229] [INSPIRE].
R.B. Mann, Entropy of rotating Misner string space-times, Phys. Rev. D 61 (2000) 084013 [hep-th/9904148] [INSPIRE].
C.V. Johnson, Thermodynamic Volumes for AdS-Taub-NUT and AdS-Taub-Bolt, Class. Quant. Grav. 31 (2014) 235003 [arXiv:1405.5941] [INSPIRE].
C.V. Johnson, The Extended Thermodynamic Phase Structure of Taub-NUT and Taub-Bolt, Class. Quant. Grav. 31 (2014) 225005 [arXiv:1406.4533] [INSPIRE].
D. Garfinkle and R.B. Mann, Generalized entropy and Noether charge, Class. Quant. Grav. 17 (2000) 3317 [gr-qc/0004056] [INSPIRE].
G. Clément, D. Gal’tsov and M. Guenouche, Rehabilitating space-times with NUTs, Phys. Lett. B 750 (2015) 591 [arXiv:1508.07622] [INSPIRE].
G. Clément, D. Gal’tsov and M. Guenouche, NUT wormholes, Phys. Rev. D 93 (2016) 024048 [arXiv:1509.07854] [INSPIRE].
G. Clément and M. Guenouche, Motion of charged particles in a NUTty Einstein-Maxwell spacetime and causality violation, Gen. Rel. Grav. 50 (2018) 60 [arXiv:1606.08457] [INSPIRE].
J.G. Miller, M.D. Kruskal and B.B. Godfrey, Taub-NUT (Newman, Unti, Tamburino) Metric and Incompatible Extensions, Phys. Rev. D 4 (1971) 2945 [INSPIRE].
R.A. Hennigar, D. Kubizň´ak and R.B. Mann, Thermodynamics of Lorentzian Taub-NUT spacetimes, Phys. Rev. D 100 (2019) 064055 [arXiv:1903.08668] [INSPIRE].
R. Durka, The first law of black hole thermodynamics for Taub-NUT spacetime, arXiv:1908.04238 [INSPIRE].
A.B. Bordo, F. Gray and D. Kubizňák, Thermodynamics and Phase Transitions of NUTty Dyons, JHEP 07 (2019) 119 [arXiv:1904.00030] [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].
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].
G. Cĺement and D. Gal’tsov, On the Smarr formulas for electrovac spacetimes with line singularities, Phys. Lett. B 802 (2020) 135270 [arXiv:1908.10617].
S.-Q. Wu and D. Wu, Thermodynamical hairs of the four-dimensional Taub-Newman-Unti-Tamburino spacetimes, Phys. Rev. D 100 (2019) 101501 [arXiv:1909.07776] [INSPIRE].
Z. Chen and J. Jiang, General Smarr relation and first law of a NUT dyonic black hole, Phys. Rev. D 100 (2019) 104016 [arXiv:1910.10107] [INSPIRE].
J.F. Plebanski and M. Demianski, Rotating, charged and uniformly accelerating mass in general relativity, Annals Phys. 98 (1976) 98 [INSPIRE].
S.W. Hawking and S.F. Ross, Duality between electric and magnetic black holes, Phys. Rev. D 52 (1995) 5865 [hep-th/9504019] [INSPIRE].
N. Altamirano, D. Kubizňák, R.B. Mann and Z. Sherkatghanad, Thermodynamics of rotating black holes and black rings: phase transitions and thermodynamic volume, Galaxies 2 (2014) 89 [arXiv:1401.2586] [INSPIRE].
M. Cvetič, 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].
R.B. Mann and C. Stelea, New Taub-NUT-Reissner-Nordstrom spaces in higher dimensions, Phys. Lett. B 632 (2006) 537 [hep-th/0508186] [INSPIRE].
A.M. Awad, Higher dimensional Taub-NUTS and Taub-Bolts in Einstein-Maxwell gravity, Class. Quant. Grav. 23 (2006) 2849 [hep-th/0508235] [INSPIRE].
M.H. Dehghani and A. Khodam-Mohammadi, Thermodynamics of Taub-NUT Black Holes in Einstein-Maxwell Gravity, Phys. Rev. D 73 (2006) 124039 [hep-th/0604171] [INSPIRE].
M.H. Dehghani and R.B. Mann, NUT-charged black holes in Gauss-Bonnet gravity, Phys. Rev. D 72 (2005) 124006 [hep-th/0510083] [INSPIRE].
M.H. Dehghani and S.H. Hendi, Taub-NUT/bolt black holes in Gauss-Bonnet-Maxwell gravity, Phys. Rev. D 73 (2006) 084021 [hep-th/0602069] [INSPIRE].
G. Dotti, J. Oliva and R. Troncoso, Exact solutions for the Einstein-Gauss-Bonnet theory in five dimensions: Black holes, wormholes and spacetime horns, Phys. Rev. D 76 (2007) 064038 [arXiv:0706.1830] [INSPIRE].
S.H. Hendi and M.H. Dehghani, Taub-NUT Black Holes in Third order Lovelock Gravity, Phys. Lett. B 666 (2008) 116 [arXiv:0802.1813] [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].
P. Bueno, P.A. Cano, R.A. Hennigar and R.B. Mann, NUTs and bolts beyond Lovelock, JHEP 10 (2018) 095 [arXiv:1808.01671] [INSPIRE].
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].
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
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2003.02268
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Bordo, A.B., Gray, F. & Kubizňák, D. Thermodynamics of rotating NUTty dyons. J. High Energ. Phys. 2020, 84 (2020). https://doi.org/10.1007/JHEP05(2020)084
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2020)084