Rigidity of quasi-Einstein metrics: The incompressible case

2023/07/03 by Eric Bahuaud, Bahuaud, Eric, Sharmila Gunasekaran +5 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2307.00738

openalex publication_date 2023/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

As part of a programme to classify quasi-Einstein metrics (M,g,X) on closed manifolds and near-horizon geometries of extreme black holes, we study such spaces when the vector field X is divergence-free but not identically zero. This condition is satisfied by left-invariant quasi-Einstein metrics on compact homogeneous spaces (including the near-horizon geometry of an extreme Myers-Perry black hole with equal angular momenta in two distinct planes), and on certain bundles over Kähler-Einstein manifolds. We find that these spaces exhibit a mild form of rigidity: they always admit a one-parameter group of isometries generated by X. Further geometrical and topological restrictions are also obtained.

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