Beijing Institute of Mathematical Sciences and Applications

Lars Andersson , Alejandro Torres-Orjuela , Xiaoran Zhang

Alex Colling

Friday, January 16, 2026 4:30 PM - 5:30 PM

A3-2-301

Zoom 787 662 9899 (BIMSA)

We will discuss the intrinsic geometry of extremal Killing horizons in a spacetime of arbitrary dimension. We establish an intrinsic analogue of Hawking’s rigidity theorem, stating that any compact cross-section of a rotating extremal horizon in a spacetime satisfying the null energy condition must admit a Killing vector field. This generalises work by Dunajski and Lucietti in the vacuum case. If the dominant energy condition is satisfied for null vectors, it follows that an extension of the associated near-horizon geometry admits an enhanced isometry group containing SO(2,1) or the 2D Poincaré group. In the latter case, we argue that the horizon should be considered doubly degenerate. We present some examples and discuss the implications for the classification problem of extremal horizons in four- and five-dimensional Einstein-Maxwell theory.

I am a PhD student under the supervision of Maciej Dunajski at the department of Applied Mathematics and Theoretical Physics at the University of Cambridge, where I completed my master's degree in 2023. I am interested in the interplay between General Relativity and Riemannian Geometry. In particular, I study extremal black holes and the geometry of their horizon cross-sections.