Inhomogeneous metrics on complex bundles in Lovelock gravity
arXiv:2504.11562 · doi:10.1103/PhysRevD.111.124016
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 Kähler 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 Kähler 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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