Abstract
We construct analytic solutions describing black holes and black branes in asymptotically Lifshitz spacetimes with arbitrary dynamical exponent z and for arbitrary number of dimensions. The model considered consists of Einstein gravity with negative cosmological constant, a scalar, and N U(1) gauge fields with dilatonic-like couplings. We study the phase diagrams and thermodynamic instabilities of the solution, and find qualitative differences between the cases with 1 ≤ z < 2, z = 2 and z > 2.
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References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].
D.T. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [SPIRES].
K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [SPIRES].
S. Kachru, X. Liu and M. Mulligan, Gravity Duals of Lifshitz-like Fixed Points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [SPIRES].
J. Maldacena, D. Martelli and Y. Tachikawa, Comments on string theory backgrounds with non-relativistic conformal symmetry, JHEP 10 (2008) 072 [arXiv:0807.1100] [SPIRES].
S.F. Ross and O. Saremi, Holographic stress tensor for non-relativistic theories, JHEP 09 (2009) 009 [arXiv:0907.1846] [SPIRES].
K. Balasubramanian and J. McGreevy, The particle number in Galilean holography, JHEP 01 (2011) 137 [arXiv:1007.2184] [SPIRES].
M. Guica, K. Skenderis, M. Taylor and B.C. van Rees, Holography for Schrödinger backgrounds, JHEP 02 (2011) 056 [arXiv:1008.1991] [SPIRES].
E.J. Brynjolfsson, U.H. Danielsson, L. Thorlacius and T. Zingg, Holographic Superconductors with Lifshitz Scaling, J. Phys. A 43 (2010) 065401 [arXiv:0908.2611] [SPIRES].
K. Balasubramanian and J. McGreevy, An analytic Lifshitz black hole, Phys. Rev. D 80 (2009) 104039 [arXiv:0909.0263] [SPIRES].
E. Ayon-Beato, A. Garbarz, G. Giribet and M. Hassaine, Lifshitz Black Hole in Three Dimensions, Phys. Rev. D 80 (2009) 104029 [arXiv:0909.1347] [SPIRES].
R.-G. Cai, Y. Liu and Y.-W. Sun, A Lifshitz Black Hole in Four Dimensional R 2 Gravity, JHEP 10 (2009) 080 [arXiv:0909.2807] [SPIRES].
D.-W. Pang, On Charged Lifshitz Black Holes, JHEP 01 (2010) 116 [arXiv:0911.2777] [SPIRES].
E. Ayon-Beato, A. Garbarz, G. Giribet and M. Hassaine, Analytic Lifshitz black holes in higher dimensions, JHEP 04 (2010) 030 [arXiv:1001.2361] [SPIRES].
M.H. Dehghani, R.B. Mann and R. Pourhasan, Charged Lifshitz Black Holes, Phys. Rev. D 84 (2011) 046002 [arXiv:1102.0578] [SPIRES].
W. Chemissany and J. Hartong, From D3-branes to Lifshitz Space-Times, arXiv:1105.0612 [SPIRES].
H. Maeda and G. Giribet, Lifshitz black holes in Brans-Dicke theory, arXiv:1105.1331 [SPIRES].
U.H. Danielsson and L. Thorlacius, Black holes in asymptotically Lifshitz spacetime, JHEP 03 (2009) 070 [arXiv:0812.5088] [SPIRES].
R.B. Mann, Lifshitz Topological Black Holes, JHEP 06 (2009) 075 [arXiv:0905.1136] [SPIRES].
G. Bertoldi, B.A. Burrington and A. Peet, Black Holes in asymptotically Lifshitz spacetimes with arbitrary critical exponent, Phys. Rev. D 80 (2009) 126003 [arXiv:0905.3183] [SPIRES].
G. Bertoldi, B.A. Burrington and A.W. Peet, Thermodynamics of black branes in asymptotically Lifshitz spacetimes, Phys. Rev. D 80 (2009) 126004 [arXiv:0907.4755] [SPIRES].
M.H. Dehghani and R.B. Mann, Lovelock-Lifshitz Black Holes, JHEP 07 (2010) 019 [arXiv:1004.4397] [SPIRES].
W.G. Brenna, M.H. Dehghani and R.B. Mann, Quasi-Topological Lifshitz Black Holes, Phys. Rev. D 84 (2011) 024012 [arXiv:1101.3476] [SPIRES].
I. Amado and A.F. Faedo, Lifshitz black holes in string theory, JHEP 07 (2011) 004 [arXiv:1105.4862] [SPIRES].
M. Taylor, Non-relativistic holography, arXiv:0812.0530 [SPIRES].
K. Balasubramanian and K. Narayan, Lifshitz spacetimes from AdS null and cosmological solutions, JHEP 08 (2010) 014 [arXiv:1005.3291] [SPIRES].
A. Donos and J.P. Gauntlett, Lifshitz Solutions of D = 10 and D = 11 supergravity, JHEP 12 (2010) 002 [arXiv:1008.2062] [SPIRES].
D. Cassani and A.F. Faedo, Constructing Lifshitz solutions from AdS, JHEP 05 (2011) 013 [arXiv:1102.5344] [SPIRES].
N. Halmagyi, M. Petrini and A. Zaffaroni, Non-Relativistic Solutions of N = 2 Gauged Supergravity, JHEP 08 (2011) 041 [arXiv:1102.5740] [SPIRES].
K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of Charged Dilaton Black Holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [SPIRES].
C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis and R. Meyer, Effective Holographic Theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [SPIRES].
S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-de Sitter Space, Commun. Math. Phys. 87 (1983) 577 [SPIRES].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [SPIRES].
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] [SPIRES].
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] [SPIRES].
C. Hoyos and P. Koroteev, On the Null Energy Condition and Causality in Lifshitz Holography, Phys. Rev. D 82 (2010) 084002 [arXiv:1007.1428] [SPIRES].
K. Copsey and R. Mann, Pathologies in Asymptotically Lifshitz Spacetimes, JHEP 03 (2011) 039 [arXiv:1011.3502] [SPIRES].
C. Niu, Y. Tian and X. Wu, Critical Phenomena and Thermodynamic Geometry of RN-AdS Black Holes, arXiv:1104.3066 [SPIRES].
D.-W. Pang, Conductivity and Diffusion Constant in Lifshitz Backgrounds, JHEP 01 (2010) 120 [arXiv:0912.2403] [SPIRES].
U.Gürsoy, E. Plauschinn, H. Stoof and S. Vandoren, Holography for Lifshitz fermions, work in progress.
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ArXiv ePrint: 1105.6335
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Tarrío, J., Vandoren, S. Black holes and black branes in Lifshitz spacetimes. J. High Energ. Phys. 2011, 17 (2011). https://doi.org/10.1007/JHEP09(2011)017
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DOI: https://doi.org/10.1007/JHEP09(2011)017