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arXiv · 2608.09847

Rotating near-horizon extreme geometries in quadratic gravity

Breno L. Giacchini·Ivan Kolář
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Abstract

Rotating near-horizon extreme solutions of quadratic gravity are analyzed combining power series expansions and numerical calculations. Restricting to geometries with symmetries of the near-horizon extreme Kerr black hole (i.e., with the $\mathrm{AdS_2}$-structure), spherical horizon topology, and equatorial reflection symmetry, we introduce conformal coordinates simplifying the field equations of Einstein--Weyl gravity, i.e., quadratic gravity with vanishing scalar curvature. Employing the Frobenius analysis, we classify all power series solutions expanded around the equator as well as the poles, and obtain the recurrence relations. With the help of numerical analysis, we study fine-tuning of the free parameter to satisfy the global constraints on regular near-horizon extreme geometries. Computations of the horizon area, horizon scalar curvature, and rotational scalar reveal strong horizon deformations in some Bachian branches. Moreover, the absence of regular Bachian near-horizon geometries above a finite horizon area suggests an upper bound on the size of the corresponding extremal rotating black holes.

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Breno L. Giacchini, Ivan Kolář. 2026-08-10. Rotating near-horizon extreme geometries in quadratic gravity. https://arxiv.org/abs/2608.09847

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