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arXiv · 2207.04014

Higher-curvature generalization of Eguchi-Hanson spaces

Cristóbal Corral·Daniel Flores-Alfonso·Gastón Giribet·Julio Oliva
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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 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.

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Cristóbal Corral, Daniel Flores-Alfonso, Gastón Giribet, Julio Oliva. 2022-11-02. Higher-curvature generalization of Eguchi-Hanson spaces. https://doi.org/10.1103/physrevd.106.084055

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