Abstract
Using G2(2) dualities we construct the most general black string solution of minimal five-dimensional ungauged supergravity. The black string has five independent parameters, namely, the magnetic one-brane charge, smeared electric zero-brane charge, boost along the string direction, energy above the BPS bound, and rotation in the transverse space. In one extremal limit it reduces to the three parameter supersymmetric string of five-dimensional minimal supergravity; in another extremal limit it reduces to the three parameter non-supersymmetric non-rotating extremal string of five-dimensional minimal supergravity. It also admits an extremal limit when it has maximal rotation in the four-dimensional transverse space. The decoupling limit of our general black string is a BTZ black hole times a two sphere. The macroscopic entropy of the string is reproduced by the Maldacena-Strominger-Witten CFT in appropriate ranges of the parameters. When the pressureless condition is imposed, our string describes the infinite radius limit of the most general class of black rings of minimal supergravity. We discuss implications our solution has for extremal and non-extremal black rings of minimal supergravity.
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References
A. Strominger and C. Vafa, Microscopic Origin of the Bekenstein-Hawking Entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [SPIRES].
S.D. Mathur, The quantum structure of black holes, Class. Quant. Grav. 23 (2006) R115 [hep-th/0510180] [SPIRES].
J.R. David, G. Mandal and S.R. Wadia, Microscopic formulation of black holes in string theory, Phys. Rept. 369 (2002) 549 [hep-th/0203048] [SPIRES].
A.W. Peet, TASI lectures on black holes in string theory, hep-th/0008241 [SPIRES].
C.G. Callan and J.M. Maldacena, D-brane Approach to Black Hole Quantum Mechanics, Nucl. Phys. B 472 (1996) 591 [hep-th/9602043] [SPIRES].
G.T. Horowitz and A. Strominger, Counting States of Near-Extremal Black Holes, Phys. Rev. Lett. 77 (1996) 2368 [hep-th/9602051] [SPIRES].
J.C. Breckenridge et al., Macroscopic and Microscopic Entropy of Near-Extremal Spinning Black Holes, Phys. Lett. B 381 (1996) 423 [hep-th/9603078] [SPIRES].
H. Elvang, R. Emparan, D. Mateos and H.S. Reall, A supersymmetric black ring, Phys. Rev. Lett. 93 (2004) 211302 [hep-th/0407065] [SPIRES].
M. Cyrier, M. Guica, D. Mateos and A. Strominger, Microscopic entropy of the black ring, Phys. Rev. Lett. 94 (2005) 191601 [hep-th/0411187] [SPIRES].
I. Bena and P. Kraus, Microscopic description of black rings in AdS/CFT, JHEP 12 (2004) 070 [hep-th/0408186] [SPIRES].
J.M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, JHEP 12 (1997) 002 [hep-th/9711053] [SPIRES].
R. Emparan and H.S. Reall, Black rings, Class. Quant. Grav. 23 (2006) R169 [hep-th/0608012] [SPIRES].
R. Emparan, Exact Microscopic Entropy of Non-Supersymmetric Extremal Black Rings, Class. Quant. Grav. 25 (2008) 175005 [arXiv:0803.1801] [SPIRES].
F. Larsen, Entropy of thermally excited black rings, JHEP 10 (2005) 100 [hep-th/0505152] [SPIRES].
M. Cvetič and D. Youm, General Rotating Five Dimensional Black Holes of Toroidally Compactified Heterotic String, Nucl. Phys. B 476 (1996) 118 [hep-th/9603100] [SPIRES].
H. Elvang and R. Emparan, Black rings, supertubes and a stringy resolution of black hole non-uniqueness, JHEP 11 (2003) 035 [hep-th/0310008] [SPIRES].
H. Elvang, R. Emparan and P. Figueras, Non-supersymmetric black rings as thermally excited supertubes, JHEP 02 (2005) 031 [hep-th/0412130] [SPIRES].
G. Compere, S. de Buyl, E. Jamsin and A. Virmani, G2 Dualities in D =5 Supergravity and Black Strings, Class. Quant. Grav. 26 (2009) 125016 [arXiv:0903.1645] [SPIRES].
A. Bouchareb et al., G2 generating technique for minimal D =5 supergravity and black rings, Phys. Rev. D 76 (2007) 104032 [arXiv:0708.2361] [SPIRES].
D.V. Gal’tsov and N.G. Scherbluk, Three-charge doubly rotating black ring, Phys. Rev. D 81 (2010) 044028 [arXiv:0912.2771] [SPIRES].
M. Tanabe, The Kerr black hole and rotating black string by intersecting M-branes, arXiv:0804.3831 [SPIRES].
S.-S. Kim, J.L. Hornlund, J. Palmkvist and A. Virmani, Extremal solutions of the S3 model and nilpotent orbits of G2(2), JHEP 08 (2010) 072 [arXiv:1004.5242] [SPIRES].
P. Breitenlohner, D. Maison and G.W. Gibbons, Four-Dimensional Black Holes from Kaluza-Klein Theories, Commun. Math. Phys. 120 (1988) 295 [SPIRES].
M.J. Duff, J.T. Liu and J. Rahmfeld, Four-dimensional string-string-string triality, Nucl. Phys. B 459 (1996) 125 [hep-th/9508094] [SPIRES].
E. Cremmer, B. Julia, H. Lü and C.N. Pope, Higher-dimensional origin of D =3 coset symmetries, hep-th/9909099 [SPIRES].
S. Giusto and A. Saxena, Stationary axisymmetric solutions of five dimensional gravity, Class. Quant. Grav. 24 (2007) 4269 [arXiv:0705.4484] [SPIRES].
D.V. Gal’tsov and N.G. Scherbluk, Generating technique for U(1)3 5D supergravity, Phys. Rev. D 78 (2008) 064033 [arXiv:0805.3924] [SPIRES].
P. Figueras, E. Jamsin, J.V. Rocha and A. Virmani, Integrability of Five Dimensional Minimal Supergravity and Charged Rotating Black Holes, Class. Quant. Grav. 27 (2010) 135011 [arXiv:0912.3199] [SPIRES].
G. Bossard, H. Nicolai and K.S. Stelle, Gravitational multi-NUT solitons, Komar masses and charges, Gen. Rel. Grav. 41 (2009) 1367 [arXiv:0809.5218] [SPIRES].
T. Harmark and N.A. Obers, General definition of gravitational tension, JHEP 05 (2004) 043 [hep-th/0403103] [SPIRES].
R.C. Myers, Stress tensors and Casimir energies in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 046002 [hep-th/9903203] [SPIRES].
G. Bossard, H. Nicolai and K.S. Stelle, Universal BPS structure of stationary supergravity solutions, JHEP 07 (2009) 003 [arXiv:0902.4438] [SPIRES].
K. Copsey and G.T. Horowitz, The role of dipole charges in black hole thermodynamics, Phys. Rev. D 73 (2006) 024015 [hep-th/0505278] [SPIRES].
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] [SPIRES].
Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, General non-extremal rotating black holes in minimal five-dimensional gauged supergravity, Phys. Rev. Lett. 95 (2005) 161301 [hep-th/0506029] [SPIRES].
M. Shmakova, Calabi-Yau Black Holes, Phys. Rev. D 56 (1997) 540 [hep-th/9612076] [SPIRES].
I. Bena, P. Kraus and N.P. Warner, Black rings in Taub-NUT, Phys. Rev. D 72 (2005) 084019 [hep-th/0504142] [SPIRES].
J.P. Gauntlett, J.B. Gutowski, C.M. Hull, S. Pakis and H.S. Reall, All supersymmetric solutions of minimal supergravity in five dimensions, Class. Quant. Grav. 20 (2003) 4587 [hep-th/0209114] [SPIRES].
I. Bena, Splitting hairs of the three charge black hole, Phys. Rev. D 70 (2004) 105018 [hep-th/0404073] [SPIRES].
R. Emparan, Rotating circular strings and infinite non-uniqueness of black rings, JHEP 03 (2004) 064 [hep-th/0402149] [SPIRES].
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].
M. Cvetič and F. Larsen, Statistical entropy of four-dimensional rotating black holes from near-horizon geometry, Phys. Rev. Lett. 82 (1999) 484 [hep-th/9805146] [SPIRES].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Blackfolds, Phys. Rev. Lett. 102 (2009) 191301 [arXiv:0902.0427] [SPIRES].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Essentials of Blackfold Dynamics, JHEP 03 (2010) 063 [arXiv:0910.1601] [SPIRES].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, New Horizons for Black Holes and Branes, JHEP 04 (2010) 046 [arXiv:0912.2352] [SPIRES].
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] [SPIRES].
H.K. Kunduri, J. Lucietti and H.S. Reall, Do supersymmetric anti-de Sitter black rings exist?, JHEP 02 (2007) 026 [hep-th/0611351] [SPIRES].
H.K. Kunduri and J. Lucietti, Near-horizon geometries of supersymmetric AdS 5 black holes, JHEP 12 (2007) 015 [arXiv:0708.3695] [SPIRES].
M.M. Caldarelli, R. Emparan and M.J. Rodriguez, Black Rings in (Anti)-deSitter space, JHEP 11 (2008) 011 [arXiv:0806.1954] [SPIRES].
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Compère, G., de Buyl, S., Stotyn, S. et al. A general black string and its microscopics. J. High Energ. Phys. 2010, 133 (2010). https://doi.org/10.1007/JHEP11(2010)133
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DOI: https://doi.org/10.1007/JHEP11(2010)133