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arXiv · 2504.11562

Inhomogeneous metrics on complex bundles in Lovelock gravity

Cristóbal Corral·Borja Diez·Daniel Flores-Alfonso·Nelson Merino·Leonardo Sanhueza
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Abstract

We consider Lovelock gravity in arbitrary, even dimensions. We find a large class of new gravitational instantons by considering extended nontrivial circle bundles over K\"ahler manifolds. Concretely, we generalize the Page-Pope metric in the presence of higher-curvature corrections of the Lovelock class. A subset of these spaces admits analytic continuation into the Lorentzian sector, producing new stationary solutions in Lovelock gravity. The geometries are fully determined by a single algebraic equation. We also obtain necessary and sufficient conditions for Lovelock-constant K\"ahler manifolds to exist in Lovelock gravity. Finally, we find a wide class of Lovelock-Maxwell solutions beyond staticity, allowing us to obtain the electrovacuum extension of these instantons.

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Cristóbal Corral, Borja Diez, Daniel Flores-Alfonso, Nelson Merino, Leonardo Sanhueza. 2025-04-15. Inhomogeneous metrics on complex bundles in Lovelock gravity. https://doi.org/10.1103/physrevd.111.124016

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