Gravitational Instanton Solutions

Lorenz-Petzold, D.

doi:10.1143/ptp.81.17

Cited by 10 publications

(18 citation statements)

References 3 publications

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“…Even in four dimensions this would be a formidable task. Some pertinent references in that case are [5,13]. However we would like to comment on the Bianchi type III situation since it may well prove relevant for various applications of Anti-de Sitter space-time.…”

Section: Other Bianchi Types: Bianchi Type IIImentioning

confidence: 99%

Single-sided domain walls in M-theory

Gibbons

Rychenkova

2000

Journal of Geometry and Physics

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Section: Other Bianchi Types: Bianchi Type IIImentioning

confidence: 99%

Single-sided domain walls in M-theory

Gibbons

Rychenkova

2000

Journal of Geometry and Physics

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“…The study of all Bianchi classes (I-IX) has been performed (for vanishing cosmological constant) in [33][34][35] and more completed recently in [36]. It turns out that only Bianchi IX exhibits a relationship with quasimodular forms.…”

Section: Self-dual Gravitational Instantons In Bianchi IXmentioning

confidence: 99%

Gravity, strings, modular and quasimodular forms

Petropoulos¹,

Vanhove²

2012

Ann. math. Blaise Pascal

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Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in the description of non-perturbative effects, in higher-order corrections of scalar-field spaces, . . . The latter often appear as gravitational instantons i.e. as special solutions of Einstein's equations. In the present lecture notes we present a class of such solutions in four dimensions, obtained by requiring (conformal) self-duality and Bianchi IX homogeneity. In this case, a vast range of configurations exist, which exhibit interesting modular properties. Examples of other Einstein spaces, without Bianchi IX symmetry, but with similar features are also given. Finally we discuss the emergence and the role of Eisenstein series in the framework of field and string theory perturbative expansions, and motivate the need for unravelling novel modular structures.

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“…The explicit integration of the evolution equations has been described a long time ago in Ref. [13,14], here this class of self-dual spaces is presented in appendix A for completeness.…”

Section: All Self-dual Solutionsmentioning

confidence: 99%

“…This can be done using the transformations (19), which now leave I α and λ i invariant as well as the canonical values of the structure constants. The integration of the resulting self-duality equations was given in ref [13,14].…”

Section: All Self-dual Solutionsmentioning

confidence: 99%

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G 3-homogeneous gravitational instantons

Bourliot¹,

Estes²,

Petropoulos³

et al. 2010

Class. Quantum Grav.

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We provide an exhaustive classification of self-dual four-dimensional gravitational instantons foliated with three-dimensional homogeneous spaces, i.e. homogeneous self-dual metrics on four-dimensional Euclidean spaces admitting 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. * bourliot@cpht.polytechnique.fr † estes@cpht.polytechnique.fr ‡ marios@cpht.polytechnique.fr § philippe.spindel@umons.ac.be

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Gravitational Instanton Solutions

Cited by 10 publications

References 3 publications

Single-sided domain walls in M-theory

Single-sided domain walls in M-theory

Gravity, strings, modular and quasimodular forms

G 3-homogeneous gravitational instantons

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