Black holes and other exact solutions in six-derivative gravity

Abstract: We study exact static spherically symmetric vacuum solutions in generic six-derivative gravity (i.e., without assuming specific relations between the coupling constants). Using modified Schwarzschild coordinates, we systematically classify solutions through Frobenius expansions, determining their number of free parameters and confirming previously known cases, such as the regular solutions at the origin. Importantly, we identify novel solutions absent in four-derivative gravity, including those with (double-degenerate) extreme horizons (and their near-horizon limits) that exist without matter sources, which may indicate the existence of regular black holes. We also find asymptotically (anti-)de Sitter spacetimes, giving rise to an effective cosmological constant. The solutions can be classified into six main classes, and, when possible, we provide the description in standard Schwarzschild coordinates, in which they split into thirteen main solution classes.