Abstract
Extreme near-horizon geometries in D = 11 supergravity preserving four supersymmetries are classified. It is shown that the Killing spinors fall into three possible orbits, corresponding to pairs of spinors defined on the spatial cross-sections of the horizon which have isotropy groups SU(3), G2, or SU(4). In each case, the conditions on the geometry and the 4-form flux are determined. The integrability conditions obtained from the Killing spinor equations are also investigated.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W. Israel, Event horizons in static vacuum space-times, Phys. Rev. 164 (1967) 1776 [INSPIRE].
B. Carter, Axisymmetric Black Hole Has Only Two Degrees of Freedom, Phys. Rev. Lett. 26 (1971) 331 [INSPIRE].
S. W. Hawking, Black holes in general relativity, Commun. Math. Phys. 25 (1972) 152 [INSPIRE].
D. C. Robinson, Uniqueness of the Kerr black hole, Phys. Rev. Lett. 34 (1975) 905 [INSPIRE].
W. Israel, Event horizons in static electrovac space-times, Commun. Math. Phys. 8 (1968) 245 [INSPIRE].
P. O. Mazur, Proof of Uniqueness of the Kerr-Newman Black Hole Solution, J. Phys. A 15 (1982) 3173 [INSPIRE].
A. Gnecchi, K. Hristov, D. Klemm, C. Toldo and O. Vaughan, Rotating black holes in 4d gauged supergravity, JHEP 01 (2014) 127 [arXiv:1311.1795] [INSPIRE].
L. Vanzo, Black holes with unusual topology, Phys. Rev. D 56 (1997) 6475 [gr-qc/9705004] [INSPIRE].
R. Emparan and H. S. Reall, A rotating black ring solution in five-dimensions, Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260] [INSPIRE].
H. Elvang, R. Emparan, D. Mateos and H. S. Reall, A supersymmetric black ring, Phys. Rev. Lett. 93 (2004) 211302 [hep-th/0407065] [INSPIRE].
H. Elvang, R. Emparan, D. Mateos and H. S. Reall, Supersymmetric black rings and three-charge supertubes, Phys. Rev. D 71 (2005) 024033 [hep-th/0408120] [INSPIRE].
V. Breunhölder and J. Lucietti, Supersymmetric black hole non-uniqueness in five dimensions, JHEP 03 (2019) 105 [arXiv:1812.07329] [INSPIRE].
V. Breunhölder and J. Lucietti, Moduli space of supersymmetric solitons and black holes in five dimensions, Commun. Math. Phys. 365 (2019) 471 [arXiv:1712.07092] [INSPIRE].
J. C. Breckenridge, R. C. Myers, A. W. Peet and C. Vafa, D-branes and spinning black holes, Phys. Lett. B 391 (1997) 93 [hep-th/9602065] [INSPIRE].
H. K. Kunduri and J. Lucietti, New thermodynamic identities for five-dimensional black holes, Class. Quant. Grav. 36 (2019) 07LT02.
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, A uniqueness theorem for stationary Kaluza-Klein black holes, Commun. Math. Phys. 302 (2011) 631 [arXiv:0812.3036] [INSPIRE].
A. Alaee, M. Khuri and H. Kunduri, Existence and Uniqueness of Stationary Solutions in 5-Dimensional Minimal Supergravity, arXiv:1904.12425 [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].
G. W. Gibbons, D. Ida and T. Shiromizu, Uniqueness and nonuniqueness of static vacuum black holes in higher dimensions, Prog. Theor. Phys. Suppl. 148 (2003) 284 [gr-qc/0203004] [INSPIRE].
J. Grover, J. B. Gutowski and W. A. Sabra, Non-existence of supersymmetric AdS5 black rings, JHEP 11 (2014) 027 [arXiv:1306.0017] [INSPIRE].
H. K. Kunduri, J. Lucietti and H. S. Reall, Do supersymmetric anti-de Sitter black rings exist?, JHEP 02 (2007) 026 [hep-th/0611351] [INSPIRE].
J. Lucietti, On the nonexistence of extreme anti-de Sitter black rings, Class. Quant. Grav. 35 (2018) 21LT01.
M. Khuri and E. Woolgar, Nonexistence of Extremal de Sitter Black Rings, Class. Quant. Grav. 34 (2017) 22LT01.
J. Gutowski and G. Papadopoulos, Index theory and dynamical symmetry enhancement of M-horizons, JHEP 05 (2013) 088 [arXiv:1303.0869] [INSPIRE].
J. Gutowski and G. Papadopoulos, M-Horizons, JHEP 12 (2012) 100 [arXiv:1207.7086] [INSPIRE].
S. Beck, U. Gran, J. Gutowski and G. Papadopoulos, All Killing Superalgebras for Warped AdS Backgrounds, JHEP 12 (2018) 047 [arXiv:1710.03713] [INSPIRE].
U. Gran, J. Gutowski and G. Papadopoulos, All superalgebras for warped AdS2 and black hole near horizon geometries, Class. Quant. Grav. 36 (2019) 235009.
J. Figueroa-O’Farrill and N. Hustler, The homogeneity theorem for supergravity backgrounds, JHEP 10 (2012) 014 [arXiv:1208.0553] [INSPIRE].
S. Klaus, Einfachzusammenhängende kompakte homogene Räume bis zur Dimension 9, Diploma Thesis, University of Mainz, Germany (1988).
J. M. Figueroa-O’Farrill and G. Papadopoulos, Maximally supersymmetric solutions of ten-dimensional and eleven-dimensional supergravities, JHEP 03 (2003) 048 [hep-th/0211089] [INSPIRE].
J. Gillard, U. Gran and G. Papadopoulos, The spinorial geometry of supersymmetric backgrounds, Class. Quant. Grav. 22 (2005) 1033 [hep-th/0410155] [INSPIRE].
H. Blaine Lawson and M.-L. Michelsohn, Spin Geometry, Princeton University Press, U.S.A. (1989).
U. Gran, J. Gutowski and G. Papadopoulos, The spinorial geometry of supersymmetric IIB backgrounds, Class. Quant. Grav. 22 (2005) 2453 [hep-th/0501177] [INSPIRE].
U. Gran, J. Gutowski, G. Papadopoulos and D. Roest, N = 31, D = 11, JHEP 02 (2007) 043 [hep-th/0610331] [INSPIRE].
U. Gran, J. Gutowski and G. Papadopoulos, Classification, geometry and applications of supersymmetric backgrounds, Phys. Rept. 794 (2019) 1 [arXiv:1808.07879] [INSPIRE].
J. Gutowski and G. Papadopoulos, Static M-horizons, JHEP 01 (2012) 005 [arXiv:1106.3085] [INSPIRE].
V. Moncrief and J. Isenberg, Symmetries of cosmological Cauchy horizons, Commun. Math. Phys. 89 (1983) 387 [INSPIRE].
H. Friedrich, I. Racz and R. M. Wald, On the rigidity theorem for space-times with a stationary event horizon or a compact Cauchy horizon, Commun. Math. Phys. 204 (1999) 691 [gr-qc/9811021] [INSPIRE].
E. Cremmer, B. Julia and J. Scherk, Supergravity Theory in Eleven-Dimensions, Phys. Lett. B 76 (1978) 409 [INSPIRE].
U. Gran, J. Gutowski and G. Papadopoulos, Index theory and dynamical symmetry enhancement near IIB horizons, JHEP 11 (2013) 104 [arXiv:1306.5765] [INSPIRE].
U. Gran, J. Gutowski, U. Kayani and G. Papadopoulos, Dynamical symmetry enhancement near IIA horizons, JHEP 06 (2015) 139 [arXiv:1409.6303] [INSPIRE].
U. Gran, J. Gutowski, U. Kayani and G. Papadopoulos, Dynamical symmetry enhancement near massive IIA horizons, Class. Quant. Grav. 32 (2015) 235004 [arXiv:1411.5286] [INSPIRE].
J. P. Gauntlett and S. Pakis, The geometry of D = 11 Killing spinors, JHEP 04 (2003) 039 [hep-th/0212008] [INSPIRE].
U. Gran, G. Papadopoulos and D. Roest, Systematics of M-theory spinorial geometry, Class. Quant. Grav. 22 (2005) 2701 [hep-th/0503046] [INSPIRE].
M. Fernández, A classification of Riemannian manifolds with structure group Spin(7), Annali Mat. Pura Appl. 143 (1986) 101.
R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt and P. A. Griffiths Exterior Differential Systems, Springer New York (1991), pp. 27–30.
G. Frobenius, Über das Pfaffsche Problem, J. für Reine und Agnew. Math. 82 (1877) 230.
B. Biran, F. Englert, B. de Wit and H. Nicolai, Gauged N = 8 Supergravity and Its Breaking From Spontaneous Compactification, Phys. Lett. B 124 (1983) 45 [Erratum ibid. 128 (1983) 461] [INSPIRE].
D. A. Salamon and T. Walpuski, Notes on the octonions, proceedings of the 23rd Gokola Geometry-Topology Conference, (2017) 1–85.
M. Fernández and A. Gray, Riemannian manifolds with structure group G2, Annali Mat. Pura Appl. 132 (1982) 19.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2104.05478
Rights and permissions
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.
About this article
Cite this article
Farotti, D., Gutowski, J. N = 4 near-horizon geometries in D = 11 supergravity. J. High Energ. Phys. 2021, 155 (2021). https://doi.org/10.1007/JHEP07(2021)155
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2021)155