G3-homogeneous gravitational instantons

F Bourliot (1) , J Estes (2) , P M Petropoulos (1) , Ph Spindel (3)

1 X - École polytechnique
2 ENS-PSL - École normale supérieure - Paris
3 Service de Mécanique et Gravitation

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.

Mots clés: Physical Sciences

Domaines: Physique [physics]

F Bourliot, J Estes, P M Petropoulos, Ph Spindel. G3-homogeneous gravitational instantons. Classical and Quantum Gravity, 2010, 27 (10), pp.105007. ⟨10.1088/0264-9381/27/10/105007⟩. ⟨hal-00594824⟩