Inhomogeneous metrics on complex bundles in Lovelock gravity
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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Cite
@article{arxiv.2504.11562,
title = {Inhomogeneous metrics on complex bundles in Lovelock gravity},
author = {Cristóbal Corral and Borja Diez and Daniel Flores-Alfonso and Nelson Merino and Leonardo Sanhueza},
journal= {arXiv preprint arXiv:2504.11562},
year = {2025}
}
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