Abstract
We explore corrections in the blackfold approach, which is a worldvolume theory capturing the dynamics of thin black branes. The corrections probe the fine structure of the branes, going beyond the approximation in which they are infinitely thin, and account for the dipole moment of worldvolume stress-energy as well as the internal spin degrees of freedom. We show that the dipole correction is induced elastically by bending a black brane. We argue that the long-wavelength linear response coefficient capturing this effect is a relativistic generalization of the Young modulus of elastic materials and we compute it analytically. Using this we draw predictions for black rings in dimensions greater than six. Furthermore, we apply our corrected blackfold equations to various multi-spinning black hole configurations in the blackfold limit, finding perfect agreement with known analytic solutions.
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References
R. Emparan, T. Harmark, V. Niarchos, N.A. Obers and M.J. Rodriguez, The phase structure of higher-dimensional black rings and black holes, JHEP 10 (2007) 110 [arXiv:0708.2181] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, World-volume effective theory for higher-dimensional black holes, Phys. Rev. Lett. 102 (2009) 191301 [arXiv:0902.0427] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Essentials of blackfold dynamics, JHEP 03 (2010) 063 [arXiv:0910.1601] [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].
M.M. Caldarelli, R. Emparan and B. Van Pol, Higher-dimensional rotating charged black holes, JHEP 04 (2011) 013 [arXiv:1012.4517] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Blackfolds in supergravity and string theory, JHEP 08 (2011) 154 [arXiv:1106.4428] [INSPIRE].
G. Grignani, T. Harmark, A. Marini, N.A. Obers and M. Orselli, Heating up the BIon, JHEP 06 (2011) 058 [arXiv:1012.1494] [INSPIRE].
R. Emparan, Blackfolds, arXiv:1106.2021 [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Blackfold approach for higher-dimensional black holes, Acta Phys. Polon. B 40 (2009) 3459 [INSPIRE].
J. Camps, R. Emparan and N. Haddad, Black brane viscosity and the Gregory-Laflamme instability, JHEP 05 (2010) 042 [arXiv:1003.3636] [INSPIRE].
M. Vasilic and M. Vojinovic, Classical spinning branes in curved backgrounds, JHEP 07 (2007) 028 [arXiv:0707.3395] [INSPIRE].
A. Papapetrou, Spinning test particles in general relativity. 1., Proc. Roy. Soc. Lond. A 209 (1951) 248.
E. Corinaldesi and A. Papapetrou, Spinning test particles in general relativity. 2, Proc. Roy. Soc. Lond. A 209 (1951) 259.
B. Carter and H. Quintana, Foundations of general relativistic high-pressure elasticity theory, Proc. Roy. Soc. Lond. A 331 (1972) 57.
M.M. Caldarelli, R. Emparan and M.J. Rodriguez, Black rings in (Anti)-deSitter space, JHEP 11 (2008) 011 [arXiv:0806.1954] [INSPIRE].
L. Landau and E.M. Lifshitz, Theory of elasticity, Course of theoretical physics. Vol. 7, Pergamon Press, Oxford U.K. (1959), pg. 134.
H. Elvang and P. Figueras, Black saturn, JHEP 05 (2007) 050 [hep-th/0701035] [INSPIRE].
J. Camps, R. Emparan, P. Figueras, S. Giusto and A. Saxena, Black rings in Taub-NUT and D0-D6 interactions, JHEP 02 (2009) 021 [arXiv:0811.2088] [INSPIRE].
M.M. Caldarelli, O.J. Dias, R. Emparan and D. Klemm, Black holes as lumps of fluid, JHEP 04 (2009) 024 [arXiv:0811.2381] [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.C. Myers and M. Perry, Black holes in higher dimensional space-times, Annals Phys. 172 (1986) 304 [INSPIRE].
G. Gibbons, M. Perry and C. Pope, The first law of thermodynamics for Kerr-anti-de Sitter black holes, Class. Quant. Grav. 22 (2005) 1503 [hep-th/0408217] [INSPIRE].
B. Kol and M. Smolkin, Black hole stereotyping: induced gravito-static polarization, JHEP 02 (2012) 010 [arXiv:1110.3764] [INSPIRE].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
R. Baier, P. Romatschke, D.T. Son, A.O. Starinets and M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP 04 (2008) 100 [arXiv:0712.2451] [INSPIRE].
V.E. Hubeny, S. Minwalla and M. Rangamani, The fluid/gravity correspondence, arXiv:1107.5780 [INSPIRE].
S. Hawking, C. Hunter and M. Taylor, Rotation and the AdS/CFT correspondence, Phys. Rev. D 59 (1999) 064005 [hep-th/9811056] [INSPIRE].
G. Gibbons, H. Lü, D.N. Page and C. Pope, The general Kerr-de Sitter metrics in all dimensions, J. Geom. Phys. 53 (2005) 49 [hep-th/0404008] [INSPIRE].
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ArXiv ePrint: 1110.4835
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Armas, J., Camps, J., Harmark, T. et al. The Young modulus of black strings and the fine structure of blackfolds. J. High Energ. Phys. 2012, 110 (2012). https://doi.org/10.1007/JHEP02(2012)110
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DOI: https://doi.org/10.1007/JHEP02(2012)110