Rod-structure classification of gravitational instantons with U(1)xU(1) isometry

Understand

The rod-structure formalism has played an important role in the study of black holes in D=4 and 5 dimensions with RxU(1)^{D-3} isometry.

• In this paper, we apply this formalism to the study of four-dimensional gravitational instantons with U(1)xU(1) isometry, which could serve as spatial backgrounds for five-dimensional black holes.
• We first introduce a stronger version of the rod structure with the rod directions appropriately normalised, and show how the regularity conditions can be read off from it.
• Requiring the absence of conical and orbifold singularities will in general impose periodicity conditions on the coordinates, and we illustrate this by considering known gravitational instantons in this class.