Abstract
We introduce a solvable system of equations that describes non-extremal multicenter solutions to six-dimensional ungauged supergravity coupled to tensor multiplets. The system involves a set of functions on a three-dimensional base metric. We obtain a family of non-extremal axisymmetric solutions that generalize the known multicenter extremal solutions, using a particular base metric that introduces a bolt. We analyze the conditions for regularity, and in doing so we show that this family does not include solutions that contain an extremal black hole and a smooth bolt. We determine the constraints that are necessary to obtain smooth horizonless solutions involving a bolt and an arbitrary number of Gibbons-Hawking centers.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].
S.D. Mathur, The Information paradox: A pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
O. Lunin and S.D. Mathur, AdS/CFT duality and the black hole information paradox, Nucl. Phys. B 623 (2002) 342 [hep-th/0109154] [INSPIRE].
I. Bena and N.P. Warner, Bubbling supertubes and foaming black holes, Phys. Rev. D 74 (2006) 066001 [hep-th/0505166] [INSPIRE].
P. Berglund, E.G. Gimon and T.S. Levi, Supergravity microstates for BPS black holes and black rings, JHEP 06 (2006) 007 [hep-th/0505167] [INSPIRE].
I. Bena, C.-W. Wang and N.P. Warner, Mergers and typical black hole microstates, JHEP 11 (2006) 042 [hep-th/0608217] [INSPIRE].
I. Bena, N. Bobev, S. Giusto, C. Ruef and N.P. Warner, An Infinite-Dimensional Family of Black-Hole Microstate Geometries, JHEP 03 (2011) 022 [Erratum ibid. 04 (2011) 059] [arXiv:1006.3497] [INSPIRE].
O. Lunin, S.D. Mathur and D. Turton, Adding momentum to supersymmetric geometries, Nucl. Phys. B 868 (2013) 383 [arXiv:1208.1770] [INSPIRE].
S. Giusto, O. Lunin, S.D. Mathur and D. Turton, D1-D5-P microstates at the cap, JHEP 02 (2013) 050 [arXiv:1211.0306] [INSPIRE].
I. Bena, S. Giusto, R. Russo, M. Shigemori and N.P. Warner, Habemus Superstratum! A constructive proof of the existence of superstrata, JHEP 05 (2015) 110 [arXiv:1503.01463] [INSPIRE].
I. Bena et al., Smooth horizonless geometries deep inside the black-hole regime, Phys. Rev. Lett. 117 (2016) 201601 [arXiv:1607.03908] [INSPIRE].
O. Lunin, J.M. Maldacena and L. Maoz, Gravity solutions for the D1-D5 system with angular momentum, hep-th/0212210 [INSPIRE].
V.S. Rychkov, D1-D5 black hole microstate counting from supergravity, JHEP 01 (2006) 063 [hep-th/0512053] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Fuzzballs with internal excitations, JHEP 06 (2007) 056 [arXiv:0704.0690] [INSPIRE].
I. Bena, M. Shigemori and N.P. Warner, Black-Hole Entropy from Supergravity Superstrata States, JHEP 10 (2014) 140 [arXiv:1406.4506] [INSPIRE].
K. Behrndt, D. Lüst and W.A. Sabra, Stationary solutions of N = 2 supergravity, Nucl. Phys. B 510 (1998) 264 [hep-th/9705169] [INSPIRE].
B. Bates and F. Denef, Exact solutions for supersymmetric stationary black hole composites, JHEP 11 (2011) 127 [hep-th/0304094] [INSPIRE].
J.B. Gutowski and H.S. Reall, General supersymmetric AdS 5 black holes, JHEP 04 (2004) 048 [hep-th/0401129] [INSPIRE].
I. Bena and N.P. Warner, One ring to rule them all . . . and in the darkness bind them?, Adv. Theor. Math. Phys. 9 (2005) 667 [hep-th/0408106] [INSPIRE].
J.P. Gauntlett and J.B. Gutowski, General concentric black rings, Phys. Rev. D 71 (2005) 045002 [hep-th/0408122] [INSPIRE].
K. Goldstein and S. Katmadas, Almost BPS black holes, JHEP 05 (2009) 058 [arXiv:0812.4183] [INSPIRE].
I. Bena, S. Giusto, C. Ruef and N.P. Warner, Multi-Center non-BPS Black Holes: the Solution, JHEP 11 (2009) 032 [arXiv:0908.2121] [INSPIRE].
G. Bossard and C. Ruef, Interacting non-BPS black holes, Gen. Rel. Grav. 44 (2012) 21 [arXiv:1106.5806] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
S.D. Mathur and D. Turton, Comments on black holes I: The possibility of complementarity, JHEP 01 (2014) 034 [arXiv:1208.2005] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, An Apologia for Firewalls, JHEP 09 (2013) 018 [arXiv:1304.6483] [INSPIRE].
S.D. Mathur and D. Turton, The flaw in the firewall argument, Nucl. Phys. B 884 (2014) 566 [arXiv:1306.5488] [INSPIRE].
I. Bena, A. Puhm and B. Vercnocke, Metastable Supertubes and non-extremal Black Hole Microstates, JHEP 04 (2012) 100 [arXiv:1109.5180] [INSPIRE].
I. Bena, A. Puhm and B. Vercnocke, Non-extremal Black Hole Microstates: Fuzzballs of Fire or Fuzzballs of Fuzz ?, JHEP 12 (2012) 014 [arXiv:1208.3468] [INSPIRE].
M. Dodelson and E. Silverstein, String-theoretic breakdown of effective field theory near black hole horizons, arXiv:1504.05536 [INSPIRE].
A. Puhm, F. Rojas and T. Ugajin, (Non-adiabatic) string creation on nice slices in Schwarzschild black holes, arXiv:1609.09510 [INSPIRE].
S.W. Hawking, M.J. Perry and A. Strominger, Soft Hair on Black Holes, Phys. Rev. Lett. 116 (2016) 231301 [arXiv:1601.00921] [INSPIRE].
V. Jejjala, O. Madden, S.F. Ross and G. Titchener, Non-supersymmetric smooth geometries and D1-D5-P bound states, Phys. Rev. D 71 (2005) 124030 [hep-th/0504181] [INSPIRE].
V. Cardoso, O.J.C. Dias, J.L. Hovdebo and R.C. Myers, Instability of non-supersymmetric smooth geometries, Phys. Rev. D 73 (2006) 064031 [hep-th/0512277] [INSPIRE].
B.D. Chowdhury and S.D. Mathur, Radiation from the non-extremal fuzzball, Class. Quant. Grav. 25 (2008) 135005 [arXiv:0711.4817] [INSPIRE].
B. Chakrabarty, D. Turton and A. Virmani, Holographic description of non-supersymmetric orbifolded D1-D5-P solutions, JHEP 11 (2015) 063 [arXiv:1508.01231] [INSPIRE].
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] [INSPIRE].
I. Bena, S. Giusto, C. Ruef and N.P. Warner, Supergravity Solutions from Floating Branes, JHEP 03 (2010) 047 [arXiv:0910.1860] [INSPIRE].
N. Bobev and C. Ruef, The Nuts and Bolts of Einstein-Maxwell Solutions, JHEP 01 (2010) 124 [arXiv:0912.0010] [INSPIRE].
G. Compere, K. Copsey, S. de Buyl and R.B. Mann, Solitons in Five Dimensional Minimal Supergravity: Local Charge, Exotic Ergoregions and Violations of the BPS Bound, JHEP 12 (2009) 047 [arXiv:0909.3289] [INSPIRE].
G. Bossard and S. Katmadas, A bubbling bolt, JHEP 07 (2014) 118 [arXiv:1405.4325] [INSPIRE].
G. Bossard and S. Katmadas, Floating JMaRT, JHEP 04 (2015) 067 [arXiv:1412.5217] [INSPIRE].
G. Bossard and H. Nicolai, Multi-black holes from nilpotent Lie algebra orbits, Gen. Rel. Grav. 42 (2010) 509 [arXiv:0906.1987] [INSPIRE].
G. Bossard, H. Nicolai and K.S. Stelle, Universal BPS structure of stationary supergravity solutions, JHEP 07 (2009) 003 [arXiv:0902.4438] [INSPIRE].
G. Bossard, 1/8 BPS Black Hole Composites, arXiv:1001.3157 [INSPIRE].
I. Bena, G. Bossard, S. Katmadas and D. Turton, Non-BPS multi-bubble microstate geometries, JHEP 02 (2016) 073 [arXiv:1511.03669] [INSPIRE].
D. Katsimpouri, A. Kleinschmidt and A. Virmani, An Inverse Scattering Construction of the JMaRT Fuzzball, JHEP 12 (2014) 070 [arXiv:1409.6471] [INSPIRE].
F. Denef, Quantum quivers and Hall/hole halos, JHEP 10 (2002) 023 [hep-th/0206072] [INSPIRE].
I. Bena, P. Kraus and N.P. Warner, Black rings in Taub-NUT, Phys. Rev. D 72 (2005) 084019 [hep-th/0504142] [INSPIRE].
I. Bena, N. Bobev and N.P. Warner, Spectral Flow and the Spectrum of Multi-Center Solutions, Phys. Rev. D 77 (2008) 125025 [arXiv:0803.1203] [INSPIRE].
G. Dall’Agata, S. Giusto and C. Ruef, U-duality and non-BPS solutions, JHEP 02 (2011) 074 [arXiv:1012.4803] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Classification of Gravitational Instanton Symmetries, Commun. Math. Phys. 66 (1979) 291 [INSPIRE].
I. Bena, G. Dall’Agata, S. Giusto, C. Ruef and N.P. Warner, Non-BPS Black Rings and Black Holes in Taub-NUT, JHEP 06 (2009) 015 [arXiv:0902.4526] [INSPIRE].
D. Mateos and P.K. Townsend, Supertubes, Phys. Rev. Lett. 87 (2001) 011602 [hep-th/0103030] [INSPIRE].
I. Bena, N. Bobev, C. Ruef and N.P. Warner, Supertubes in Bubbling Backgrounds: Born-Infeld Meets Supergravity, JHEP 07 (2009) 106 [arXiv:0812.2942] [INSPIRE].
F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [INSPIRE].
G. Bossard and S. Katmadas, non-BPS walls of marginal stability, JHEP 10 (2013) 179 [arXiv:1309.3236] [INSPIRE].
S. Giusto, S.D. Mathur and A. Saxena, Dual geometries for a set of 3-charge microstates, Nucl. Phys. B 701 (2004) 357 [hep-th/0405017] [INSPIRE].
S. Giusto, S.D. Mathur and A. Saxena, 3-charge geometries and their CFT duals, Nucl. Phys. B 710 (2005) 425 [hep-th/0406103] [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
ArXiv ePrint: 1611.03500
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Bena, I., Bossard, G., Katmadas, S. et al. Bolting multicenter solutions. J. High Energ. Phys. 2017, 127 (2017). https://doi.org/10.1007/JHEP01(2017)127
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2017)127