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

  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},
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… 

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

  • W. Wylie
  • Physics
    Letters 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

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