A new analytic framework makes it possible to build, in a unified way, the geometries of rotating black holes when the assumptions of vacuum general relativity are dropped. The work describes how to obtain stationary, axisymmetric deformations of the Kerr black hole from its tidal curvature and physical sources, overcoming a limitation that until now forced numerical treatments or expansions in the rotation parameter.

As a demonstration, the authors obtain closed-form solutions for six higher-curvature interactions, at leading order in the couplings and for generic subextremal spin. The method does not rely on slow-rotation expansions, numerical fitting or mode decompositions, which represents a substantial gain over earlier constructions that solved the equations mode by mode.

The solutions pass stringent checks: they satisfy the field equations, reproduce previous mode-by-mode constructions and match known analytic predictions for horizon quantities. A standout finding is that the chirality of the interactions organizes the analytic structure of the solutions, a pattern the authors expect to extend to a large class of purely metric higher-curvature theories.

The framework opens a systematic route to black-hole geometries in beyond-Einstein theories and in 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.