Some geometric properties of generalized $$\varphi $$-vacuum static spaces [Some geometric properties of generalized φ-vacuum static spaces]

In this paper we study the geometry of generalized φ-vacuum static spaces, proving estimates for the φ-scalar curvature and for the first eigenvalue of the Jacobi operator, and also rigidity under various geometric ass be a compact manifold. umptions; in particular, we prove a result related to the famous Cosmic no-hair conjecture of Boucher, Gibbons and Horowitz.