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arXiv · 2610.37515

One Method to Find Them All: Analytic Black Holes beyond Einstein

Dongjun Li·Jierui Hu·Nicolás Yunes
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Abstract

Rotating black holes offer powerful probes of gravity, but constructing their geometries beyond vacuum general relativity remains challenging. Here we develop a unified framework for constructing stationary, axisymmetric deformations of Kerr from their tidal curvature and physical sources. As a demonstration, we obtain closed-form solutions for six higher-curvature interactions at leading order in the couplings and for generic subextremal spin, without slow-rotation expansions, numerical fitting, or mode decomposition. The solutions pass stringent checks against the field equations, previous mode-by-mode constructions, and known analytic predictions for horizon quantities. We find that the chirality of the interactions organizes the analytic structure of these solutions, a pattern that likely extends to a large class of purely metric higher-curvature theories. Our framework opens a systematic route to black-hole geometries in beyond-Einstein theories and perturbative astrophysical environments. These geometries provide a foundation for strong-field tests with gravitational waves and other observational channels, such as black-hole images and X-ray spectroscopy, as well as theoretical studies of near-extremal black holes.

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Dongjun Li, Jierui Hu, Nicolás Yunes. 2026-10-27. One Method to Find Them All: Analytic Black Holes beyond Einstein. https://arxiv.org/abs/2610.37515

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