G3-homogeneous gravitational instantons

[en] We provide an exhaustive classification of self-dual four-dimensional grav- itational instantons foliated with three-dimensional homogeneous spaces, i.e. homogeneous self-dual metrics on four-dimensional Euclidean spaces admit- ting a Bianchi simply transitive isometry group. The classification pattern is based on the algebra homomorphisms relating the Bianchi group and the duality group SO(3). New and general solutions are found for Bianchi III.

Disciplines :

Physics

Author, co-author :

Bourliot, F.

Estes, J.

Petropoulos, P. M.

Spindel, Philippe ; Université de Mons > Faculté des Sciences > Mécanique et gravitation

Language :

English

Title :

G3-homogeneous gravitational instantons

Publication date :

01 January 2010

Journal title :

Classical and Quantum Gravity

ISSN :

0264-9381

Publisher :

Institute of Physics Publishing, United Kingdom

Volume :

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Commentary :

Z105007,2010 e-Print: arXiv:0912.4848 [hep-th],Bibliographic Code:2010CQGra..27j5007B

Available on ORBi UMONS :

since 10 June 2010

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Bibliography

Belavin A A, Polyakov A M, Shvarts A S and Tyupkin Yu S 1975 Pseudoparticle solutions of the Yang-Mills equations Phys. Lett. 59B 85
Eguchi T and Hanson A J 1978 Asymptotically flat self-dual solutions to Euclidean gravity Phys. Lett. 74B 249
Eguchi T and Hanson A J 1979 Selfdual solutions to Euclidean gravity Ann. Phys. 120 82
Newman E T, Tamburino L and Unti T J 1963 Empty-space generalization of the Schwarzschild metric J. Math. Phys. 4 915
Belinsky V A, Gibbons G W, Page D N and Pope C N 1978 Asymptotically Euclidean Bianchi IX metrics in quantum gravity Phys. Lett. 76B 433
Gibbons G W and Pope C N 1979 The positive action conjecture and asymptotically Euclidean metrics In quantum gravity Commun. Math. Phys. 66 267
Atiyah M F, Hitchin N J and Singer I M 1978 Self-duality in four-dimensional Riemannian geometry Proc. R. Soc. A 362 425
Takhtajan L A 1992 A simple example of modular forms as tau functions for integrable equations Theor. Math. Phys. 93 1308
Takhtajan L A 1992 A simple example of modular forms as tau functions for integrable equations Teor. Mat. Fiz. 93 330
Darboux G 1878 Mémoire sur la théorie des coordonnées curvilignes et des systèmes orthogonaux Ann. Ec. Normale Supér. 7 101
Halphen G-H 1881 Sur un système d'équations différentielles C. R. Acad. Sc. Paris 92 1001
Halphen G-H 1881 Sur certains systèmes d'équations différentielles C. R. Acad. Sc. Paris 92 1004
Petropoulos P M http://wwwth.mppmu.mpg.de/members/strings/Ricci/ricci- files/Talks/Petropoulos.pdf
Lorenz D 1983 Gravitational instanton solutions for Bianchi types I-IX Acta Phys. Pol. 14 791
Lorenz-Petzold D 1989 Gravitational instanton solutions Prog. Theor. Phys. 81 17
Kasner E 1921 Geometrical theorems on Einstein's cosmological equations Am. J. Math. 43 217
Bourliot F, Estes J, Petropoulos P M and Spindel Ph 2009 Gravitational instantons, self-duality and geometric flows arXiv:0906.4558 [hep-th]
Pedersen H 1986 Einstein metrics, spinning top motions and monopoles Math. Ann. 274 35
Spindel Ph 1985 Gravity before supergravity Supersymmetry (NATO ASI Series, Series B: Physics vol 125) ed K Dietz, R Flume, G v Gehlen and V Rittenberg (New York and London: Plenum)
Gibbons G W and Hawking S W 1979 Classification of gravitational instanton symmetries Commun. Math. Phys. 66 291
Atiyah M F and Hitchin N J 1985 Low-energy scattering of non-Abelian magnetic monopoles Phil. Trans. R. Soc. A 315 459
Atiyah M F and Hitchin N J 1985 Low-energy scattering of non-Abelian monopoles Phys. Lett. 107A 21
Barrow J D, Gaspar Y and Saffin P M 2000 Some exact non-vacuum Bianchi VI(0) and VII(0) instantons Class. Quantum Grav. 17 1435 (arXiv:gr-qc/9905100)
Saha B 2007 Interacting spinor and scalar fields in Bianchi cosmology arXiv:gr-qc/0701059
Saha B and Rikhvitsky V 2006 Bianchi type I universe with viscous fluid: a qualitative analysis Physica D 219 168 (arXiv:gr-qc/0410056)
Spokoiny B L 1982 The effect of the electromagnetic fields on the evolution of homogeneous cosmological models near the singularity Gen. Rel. Grav. 14 279
Fay S 2000 Sufficient conditions for curvature invariants to avoid divergences in hyperextended scalar tensor theory for Bianchi models Class. Quantum Grav. 17 2663 (arXiv:gr-qc/0309087)