Abstract
We study the surface transport properties of stationary localized configurations of relativistic fluids to the first two non-trivial orders in a derivative expansion. By demanding that these finite lumps of relativistic fluid are described by a thermal partition function with arbitrary stationary background metric and gauge fields, we are able to find several constraints among surface transport coefficients. At leading order, besides recovering the surface thermodynamics, we obtain a generalization of the Young-Laplace equation for relativistic fluid surfaces, by considering a temperature dependence in the surface tension, which is further generalized in the context of superfluids. At the next order, for uncharged fluids in 3+1 dimensions, we show that besides the 3 independent bulk transport coefficients previously known, a generic localized configuration is characterized by 3 additional surface transport coefficients, one of which may be identified with the surface modulus of rigidity. Finally, as an application, we study the effect of temperature dependence of surface tension on some explicit examples of localized fluid configurations, which are dual to certain non-trivial black hole solutions via the AdS/CFT correspondence.
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References
L. Landau and E. Lifshitz, Textbook on theoretical physics. Vol. 6: fluid mechanics, Butterworth-Heinemann, U.K. (1987).
D.T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and A. Yarom, A theory of first order dissipative superfluid dynamics, JHEP 05 (2014) 147 [arXiv:1105.3733] [INSPIRE].
S. Bhattacharyya, Constraints on the second order transport coefficients of an uncharged fluid, JHEP 07 (2012) 104 [arXiv:1201.4654] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Adiabatic hydrodynamics: the eightfold way to dissipation, JHEP 05 (2015) 060 [arXiv:1502.00636] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, The fluid manifesto: emergent symmetries, hydrodynamics and black holes, JHEP 01 (2016) 184 [arXiv:1510.02494] [INSPIRE].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam and P. Surowka, Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].
J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya and S. Minwalla, Dissipative superfluid dynamics from gravity, JHEP 04 (2011) 125 [arXiv:1101.3332] [INSPIRE].
C.P. Herzog, N. Lisker, P. Surowka and A. Yarom, Transport in holographic superfluids, JHEP 08 (2011) 052 [arXiv:1101.3330] [INSPIRE].
O. Aharony, S. Minwalla and T. Wiseman, Plasma-balls in large-N gauge theories and localized black holes, Class. Quant. Grav. 23 (2006) 2171 [hep-th/0507219] [INSPIRE].
J. Armas, How fluids bend: the elastic expansion for higher-dimensional black holes, JHEP 09 (2013) 073 [arXiv:1304.7773] [INSPIRE].
J. Armas, (Non)-dissipative hydrodynamics on embedded surfaces, JHEP 09 (2014) 047 [arXiv:1312.0597] [INSPIRE].
J. Armas and T. Harmark, Constraints on the effective fluid theory of stationary branes, JHEP 10 (2014) 063 [arXiv:1406.7813] [INSPIRE].
D. Bombardelli, D. Fioravanti and R. Tateo, Thermodynamic Bethe ansatz for planar AdS/CFT: a proposal, J. Phys. A 42 (2009) 375401 [arXiv:0902.3930] [INSPIRE].
P. Canham, The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell, J. Theor. Biol. 26 (1970) 61.
U. Seifert, Configurations of fluid membranes and vesicles, Adv. Phys. 46 (1997) 13.
N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Jain, S. Minwalla and T. Sharma, Constraints on fluid dynamics from equilibrium partition functions, JHEP 09 (2012) 046 [arXiv:1203.3544] [INSPIRE].
K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].
S. Jain and T. Sharma, Anomalous charged fluids in 1 + 1d from equilibrium partition function, JHEP 01 (2013) 039 [arXiv:1203.5308] [INSPIRE].
N. Banerjee, S. Dutta, S. Jain, R. Loganayagam and T. Sharma, Constraints on anomalous fluid in arbitrary dimensions, JHEP 03 (2013) 048 [arXiv:1206.6499] [INSPIRE].
S. Bhattacharyya, S. Jain, S. Minwalla and T. Sharma, Constraints on superfluid hydrodynamics from equilibrium partition functions, JHEP 01 (2013) 040 [arXiv:1206.6106] [INSPIRE].
S. Bhattacharyya, Entropy current and equilibrium partition function in fluid dynamics, JHEP 08 (2014) 165 [arXiv:1312.0220] [INSPIRE].
S. Bhattacharyya, Entropy current from partition function: one example, JHEP 07 (2014) 139 [arXiv:1403.7639] [INSPIRE].
K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Parity-violating hydrodynamics in 2 + 1 dimensions, JHEP 05 (2012) 102 [arXiv:1112.4498] [INSPIRE].
S. Lahiri and S. Minwalla, Plasmarings as dual black rings, JHEP 05 (2008) 001 [arXiv:0705.3404] [INSPIRE].
B. Carter, Essentials of classical brane dynamics, Int. J. Theor. Phys. 40 (2001) 2099 [gr-qc/0012036] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Essentials of blackfold dynamics, JHEP 03 (2010) 063 [arXiv:0910.1601] [INSPIRE].
J. Bhattacharya and S. Lahiri, Lumps of plasma in arbitrary dimensions, JHEP 08 (2010) 073 [arXiv:0903.4734] [INSPIRE].
M.M. Caldarelli, O.J.C. Dias, R. Emparan and D. Klemm, Black holes as lumps of fluid, JHEP 04 (2009) 024 [arXiv:0811.2381] [INSPIRE].
L.D. Landau, Theory of the superfluidity of helium II, Phys. Rev. 60 (1941) 356.
L. Tisza, The theory of liquid helium, Phys. Rev. 72 (1947) 838 [INSPIRE].
J. Bhattacharya, S. Bhattacharyya and M. Rangamani, Non-dissipative hydrodynamics: effective actions versus entropy current, JHEP 02 (2013) 153 [arXiv:1211.1020] [INSPIRE].
M. Vasilic and M. Vojinovic, Classical spinning branes in curved backgrounds, JHEP 07 (2007) 028 [arXiv:0707.3395] [INSPIRE].
S. Bhardwaj and J. Bhattacharya, Thermodynamics of plasmaballs and plasmarings in 3 + 1 dimensions, JHEP 03 (2009) 101 [arXiv:0806.1897] [INSPIRE].
N. Banerjee, S. Dutta and A. Jain, Null fluids — a new viewpoint of Galilean fluids, Phys. Rev. D 93 (2016) 105020 [arXiv:1509.04718] [INSPIRE].
N. Banerjee, S. Dutta and A. Jain, Equilibrium partition function for nonrelativistic fluids, Phys. Rev. D 92 (2015) 081701 [arXiv:1505.05677] [INSPIRE].
N. Banerjee, S. Dutta, A. Jain and D. Roychowdhury, Entropy current for non-relativistic fluid, JHEP 08 (2014) 037 [arXiv:1405.5687] [INSPIRE].
R. Emparan and R.C. Myers, Instability of ultra-spinning black holes, JHEP 09 (2003) 025 [hep-th/0308056] [INSPIRE].
J. Armas and N.A. Obers, Blackfolds in (anti)-de Sitter backgrounds, Phys. Rev. D 83 (2011) 084039 [arXiv:1012.5081] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, New horizons for black holes and branes, JHEP 04 (2010) 046 [arXiv:0912.2352] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Thermodynamics, gravitational anomalies and cones, JHEP 02 (2013) 088 [arXiv:1207.5824] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Anomaly inflow and thermal equilibrium, JHEP 05 (2014) 134 [arXiv:1310.7024] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Chern-Simons terms from thermal circles and anomalies, JHEP 05 (2014) 110 [arXiv:1311.2935] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, The eightfold way to dissipation, Phys. Rev. Lett. 114 (2015) 201601 [arXiv:1412.1090] [INSPIRE].
M. Crossley, P. Glorioso and H. Liu, Effective field theory of dissipative fluids, arXiv:1511.03646 [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Topological σ-models & dissipative hydrodynamics, JHEP 04 (2016) 039 [arXiv:1511.07809] [INSPIRE].
J.W. Cahn and J.E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28 (1958) 258.
J. Armas, J. Gath and N.A. Obers, Electroelasticity of charged black branes, JHEP 10 (2013) 035 [arXiv:1307.0504] [INSPIRE].
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Armas, J., Bhattacharya, J. & Kundu, N. Surface transport in plasma-balls. J. High Energ. Phys. 2016, 15 (2016). https://doi.org/10.1007/JHEP06(2016)015
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DOI: https://doi.org/10.1007/JHEP06(2016)015