Freitag, 30.01.2026: Static Black Holes with a Negative Cosmological Constant
PhD Brian Harvie (Universität Kopenhagen)
The classification of stationary black hole solutions of the Einstein field equations, broadly referred to as the "no-hair conjecture", is a challenging and fundamental line of research in general relativity. The problem is more tractable for black hole spacetimes which are static, but even under this stronger assumption the existing results are mostly limited to static black holes with zero or positive cosmological constant. In this talk, I will present a geometric inequality for isolated static vacuum black holes with a negative cosmological constant which has far-reaching implications for their geometry and uniqueness.
The inequality relates the surface gravity, area, and topology of a horizon in a static spacetime to its conformal infinity, and equality is achieved only by the Kottler black holes. From this, we deduce several new static uniqueness theorems for Kottler. Namely, we show: (1) the Kottler black hole over the sphere which minimizes surface gravity is unique, (2) the Kottler black hole over the torus is unique, assuming the horizons have non-spherical topology, and (3) uniqueness for the higher-genus Kottler black holes is equivalent to the Riemannian Penrose inequality. This is based on joint work with Ye-Kai Wang.
| Uhrzeit: |
14:00 |
| Ort: |
7E02 (Hörsaalzentrum) |
| Gruppe: |
4. ANGEL Meeting |
| Einladender: |
Carla Cederbaum |
Freitag, 30.01.2026: Quaternion Kähler manifolds of non-negative sectional curvature
Profl Dr. Uwe Semmelmann (Universität Stuttgart)
Quaternion Kähler manifolds, i.e., Riemannian manifolds with
holonomy contained in Sp(m)Sp(1), are Einstein. In the case of
positive scalar curvature, there is a longstanding
conjecture by LeBrun and Salamon stating that all such manifolds should
be symmetric. So far, the conjecture has been confirmed only up to
dimension 12.
In the first part of my talk I will give an introduction to the
geometry of quaternion Kähler manifolds of positive scalar curvature
In the second part I will make a few remarks on the proof of the conjecture
under the additional assumption of non-negative sectional curvature.
This extends earlier work by Berger, who proved that quaternion Kähler
manifolds of positive sectional curvature are isometric to
the quaternionic projective space.
My talk is based on a joint article with Simon Brendle and on
earlier work by Simon Brendle.
| Uhrzeit: |
16:45 |
| Ort: |
7E02 (Hörsaalzentrum) |
| Gruppe: |
4. ANGEL Meeting |
| Einladender: |
Carla Cederbaum |
