Higher-curvature generalization of Eguchi-Hanson spaces

Abstract

We construct higher-dimensional generalizations of the Eguchi-Hanson gravitational instanton in the presence of higher-curvature deformations of general relativity. These spaces are solutions to Einstein gravity supplemented with the dimensional extension of the quadratic Chern-Gauss-Bonnet invariant in arbitrary even dimension $D=2m\ge 4$, and they are constructed out of non-trivial fibrations over $(2m-2)$-dimensional Kähler-Einstein manifolds. Different aspects of these solutions are analyzed; among them, the regularization of the on-shell Euclidean action by means of the addition of topological invariants. We also consider higher-curvature corrections to the gravity action that are cubic in the Riemann tensor and explicitly construct Eguchi-Hanson type solutions for such.

v1: 17 pages; v2: Comments added, 18 pages, matches published version in Physical Review D

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Cited by in corpus (3)

• Phase Transitions and Stability of Eguchi-Hanson-AdS Solitons
• Axial anomaly in nonlinear conformal electrodynamics
• Inhomogeneous metrics on complex bundles in Lovelock gravity