One Method to Find Them All: Analytic Black Holes beyond Einstein
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.
Related
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- Tidal Response Beyond the Background Geometry in Einstein-Euler-Heisenberg Black Holes
- Nonexistence of Multiple Black Holes in Stationary Analytic Vacuum spacetimes
- Analytic Metric for Rotating Black Holes in Higher-Derivative Gravity
- Cloudy black-hole configurations of the composed Einstein-Yang-Mills-Higgs field theory: Analytic treatment
BibTeX
@misc{li2026method,
title = {{One Method to Find Them All: Analytic Black Holes beyond Einstein}},
author = {Dongjun Li and Jierui Hu and Nicolás Yunes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37515},
eprint = {2610.37515},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37515},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - One Method to Find Them All: Analytic Black Holes beyond Einstein
AU - Dongjun Li
AU - Jierui Hu
AU - Nicolás Yunes
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37515
UR - https://arxiv.org/abs/2610.37515
AB - 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.
ER -