Higher-curvature generalization of Eguchi-Hanson spaces

TL;DR

This paper constructs higher-dimensional Eguchi-Hanson gravitational instantons within higher-curvature gravity theories, analyzing their properties and regularization, and extends solutions to include cubic Riemann tensor corrections.

Contribution

It introduces new higher-dimensional Eguchi-Hanson solutions in higher-curvature gravity, including quadratic and cubic Riemann tensor corrections, expanding the understanding of gravitational instantons.

Findings

Constructed solutions in arbitrary even dimensions with quadratic curvature terms.

Analyzed regularization of Euclidean action using topological invariants.

Extended solutions to include cubic Riemann tensor corrections.

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 $D=2m\geq 4$, and they are constructed out of non-trivial fibrations over $(2m-2)$-dimensional K\"ahler-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.