# Static near-horizon geometries and rigidity of quasi-Einstein manifolds

@article{Bahuaud2022StaticNG, title={Static near-horizon geometries and rigidity of quasi-Einstein manifolds}, author={Eric Bahuaud and Sharmila Arcot Gunasekaran and Hari K. Kunduri and Eric Woolgar}, journal={Letters in Mathematical Physics}, year={2022}, volume={112} }

Static vacuum near-horizon geometries are solutions (M, g, X) of a certain quasi-Einstein equation on a closed manifold M, where g is a Riemannian metric and X is a closed 1-form. It is known that when the cosmological constant vanishes, there is rigidity: X vanishes and consequently g is Ricci-flat. We study this form of rigidity for all signs of the cosmological constant. It has been asserted that this rigidity also holds when the cosmological constant is negative, but we exhibit a counter…

## 2 Citations

### Rigidity of compact static near-horizon geometries with negative cosmological constant

- PhysicsLetters in Mathematical Physics
- 2023

In this note, we show that compact static near-horizon geometries with negative cosmological constant are either Einstein or the product of a circle and an Einstein metric. Chruściel, Reall, and Todd…

### Bakry–Émery Ricci curvature, X-minimal hypersurfaces, and near horizon geometries

- MathematicsJournal of Mathematical Physics
- 2023

Motivated by the extreme black hole near horizon geometry equation and the Ellis–Ehlers equation of mathematical cosmology, we prove a Bakry–Émery generalization of a theorem of Frankel that closed…

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