Rigidity of quasi-Einstein metrics: the incompressible case

被引：4

作者：

Bahuaud, Eric ^{[1
]}

Gunasekaran, Sharmila ^{[2
]}

Kunduri, Hari K. ^{[3
,4
]}

Woolgar, Eric ^{[5
,6
]}

机构：

[1] Seattle Univ, Dept Math, Seattle, WA 98122 USA

[2] Fields Inst Res Math Sci, 222 Coll St, Toronto, ON M5T 3J1, Canada

[3] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4K1, Canada

[4] McMaster Univ, Dept Phys & Astron, Hamilton, ON L8S 4K1, Canada

[5] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[6] Univ Alberta, Theoret Phys Inst, Edmonton, AB T6G 2G1, Canada

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2023年 / 114卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Near-horizon geometry; Extreme black holes; Quasi-Einstein equation; NONEXISTENCE;

D O I：

10.1007/s11005-023-01753-0

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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 Kahler-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.

引用

页数：17

共 16 条

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