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

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 …