New restrictions on the topology of extreme black holes

2018/04/30 by Marcus Khuri, Eric Woolgar, William Wylie
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Betti number #Black Holes and Theoretical Physics #Combinatorics #Cosmology and Gravitation Theories #Dimension (graph theory) #Einstein #Geometry #Geometry and topology #Horizon #Infinity #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Symmetry (geometry) #Theoretical physics #Topology (electrical circuits) #gr-qc #hep-th #math.DG

paper · pdf · doi:10.1007/s11005-018-1121-9

published as Lett. Math. Phys., 109 (2019), no. 3, 661-673 · 11 pages; minor improvements

arxiv created 2018/07/26 · openalex publication_date 2018/07/28 · arxiv updated 2021/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We provide bounds on the first Betti number and structure results for the fundamental group of horizon cross-sections for extreme stationary vacuum black holes in arbitrary dimension, without additional symmetry hypotheses. This is achieved by exploiting a correspondence between the associated near-horizon geometries and the mathematical notion of m-quasi Einstein metrics, in addition to generalizations of the classical splitting theorem from Riemannian geometry. Consequences are analyzed and refined classifications are given for the possible topologies of these black holes.

Citations

• Optimal Transport
• The splitting theorem for manifolds of nonnegative Ricci curvature
• On non-existence of static vacuum black holes with degenerate components of the event horizon
• Black strings andp-branes are unstable
• The Large Scale Structure of Space-Time
• Positive scalar curvature and the Dirac operator on complete riemannian manifolds
• Black hole uniqueness theorems in higher dimensional spacetimes