2025/12/11 by Alex Colling, Colling, Alex · 1 citation
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2512.10200
We prove an intrinsic analogue of Hawking's rigidity theorem for extremal horizons in arbitrary dimensions: any compact cross-section of a rotating extremal horizon in a spacetime satisfying the null energy condition must admit a Killing vector field. If the dominant energy condition is satisfied for null vectors, it follows that an extension of the near-horizon geometry admits an enhanced isometry group containing SO(2,1) or the 2D Poincaré group ℝ2 \rtimes SO(1,1). In the latter case, the associated Aretakis instability for a massless scalar field is shifted by one order in the derivatives of the field transverse to the horizon. We consider a broad class of examples including Einstein-Maxwell(-Chern-Simons) theory and Yang-Mills theory coupled to charged matter. In these examples we show that the symmetries are inherited by the matter fields.