Abstract
STU supergravity becomes an integrable system for solutions that effectively only depend on two variables. This class of solutions includes the Kerr solution and its charged generalizations that have been studied in the literature. We here present an inverse scattering method that allows to systematically construct solutions of this integrable system. The method is similar to the one of Belinski and Zakharov for pure gravity but uses a different linear system due to Breitenlohner and Maison and here requires some technical modifications. We illustrate this method by constructing a four-charge rotating solution from flat space. A generalization to other set-ups is also discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V.A. Belinsky and V.E. Zakharov, Integration of the Einstein Equations by the Inverse Scattering Problem Technique and the Calculation of the Exact Soliton Solutions, Sov. Phys. JETP 48 (1978) 985 [Zh. Eksp. Teor. Fiz. 75 (1978) 1953] [INSPIRE].
V.A. Belinsky and V.E. Sakharov, Stationary Gravitational Solitons with Axial Symmetry, Sov. Phys. JETP 50 (1979) 1 [Zh. Eksp. Teor. Fiz. 77 (1979) 3] [INSPIRE].
V. Belinski and E. Verdaguer, Gravitational solitons, Cambridge Univ. Press, U.K., 2001.
R. Emparan and H.S. Reall, Black Holes in Higher Dimensions, Living Rev. Rel. 11 (2008) 6 [arXiv:0801.3471] [INSPIRE].
H. Iguchi, K. Izumi and T. Mishima, Systematic solution-generation of five-dimensional black holes, Prog. Theor. Phys. Suppl. 189 (2011) 93 [arXiv:1106.0387] [INSPIRE].
J.V. Rocha, M.J. Rodriguez, O. Varela and A. Virmani, Charged black rings from inverse scattering, Gen. Rel. Grav. 45 (2013) 2099 [arXiv:1305.4969] [INSPIRE].
J. Ehlers, Transformations of static exterior solutions of Einstein’s gravitational field equations into different solutions by means of conformal mappings, in Les Théories Physiques de la Gravitation, CNRS, Paris, 1959, pg. 275.
E. Cremmer and B. Julia, The SO(8) Supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].
N. Marcus and J.H. Schwarz, Three-Dimensional Supergravity Theories, Nucl. Phys. B 228 (1983)145 [INSPIRE].
P. Breitenlohner, D. Maison and G.W. Gibbons, Four-Dimensional Black Holes from Kaluza-Klein Theories, Commun. Math. Phys. 120 (1988) 295 [INSPIRE].
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] [INSPIRE].
P. Breitenlohner and D. Maison, On the Geroch Group, Annales Poincaré Phys. Theor. 46 (1987)215 [INSPIRE].
D. Katsimpouri, A. Kleinschmidt and A. Virmani, Inverse Scattering and the Geroch Group, JHEP 02 (2013) 011 [arXiv:1211.3044] [INSPIRE].
P. Breitenlohner and D. Maison, Solitons in Kaluza-Klein Theories, unpublished notes, June 1986.
M.J. Duff, J.T. Liu and J. Rahmfeld, Four-dimensional string-string-string triality, Nucl. Phys. B 459 (1996) 125 [hep-th/9508094] [INSPIRE].
K. Behrndt, R. Kallosh, J. Rahmfeld, M. Shmakova and W.K. Wong, STU black holes and string triality, Phys. Rev. D 54 (1996) 6293 [hep-th/9608059] [INSPIRE].
Z.-W. Chong, M. Cvetič, H. Lü and C.N. Pope, Charged rotating black holes in four-dimensional gauged and ungauged supergravities, Nucl. Phys. B 717 (2005) 246 [hep-th/0411045] [INSPIRE].
M. Cvetič, G.W. Gibbons, C.N. Pope and Z.H. Saleem, Electrodynamics of Black Holes in STU Supergravity, arXiv:1310.5717 [INSPIRE].
D.D.K. Chow and G. Compère, Seed for general rotating non-extremal black holes of N = 8 supergravity, Class. Quant. Grav. 31 (2014) 022001 [arXiv:1310.1925] [INSPIRE].
M. Cvetič and D. Youm, Entropy of nonextreme charged rotating black holes in string theory, Phys. Rev. D 54 (1996) 2612 [hep-th/9603147] [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, Y. Michel and B. Pioline, Extremal black holes, nilpotent orbits and the true fake superpotential, JHEP 01 (2010) 038 [arXiv:0908.1742] [INSPIRE].
H. Nicolai, Two-dimensional gravities and supergravities as integrable system, Lect. Notes Phys. 396 (1991) 231, in Proceedings of Recent aspects of quantum fields, pg. 43, Schladming, May 1991.
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].
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].
T. Harmark, Stationary and axisymmetric solutions of higher-dimensional general relativity, Phys. Rev. D 70 (2004) 124002 [hep-th/0408141] [INSPIRE].
S. Hollands and S. Yazadjiev, Uniqueness theorem for 5-dimensional black holes with two axial Killing fields, Commun. Math. Phys. 283 (2008) 749 [arXiv:0707.2775] [INSPIRE].
Y. Chen and E. Teo, Rod-structure classification of gravitational instantons with U(1) × U(1) isometry, Nucl. Phys. B 838 (2010) 207 [arXiv:1004.2750] [INSPIRE].
S.D. Mathur, The Fuzzball proposal for black holes: An Elementary review, Fortsch. Phys. 53 (2005)793 [hep-th/0502050] [INSPIRE].
I. Bena and N.P. Warner, Resolving the Structure of Black Holes: Philosophizing with a Hammer, arXiv:1311.4538 [INSPIRE].
A. Virmani, Subtracted Geometry From Harrison Transformations, JHEP 07 (2012) 086 [arXiv:1203.5088] [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: 1311.7018
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
Katsimpouri, D., Kleinschmidt, A. & Virmani, A. An inverse scattering formalism for STU supergravity. J. High Energ. Phys. 2014, 101 (2014). https://doi.org/10.1007/JHEP03(2014)101
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2014)101