Abstract 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.
Branca et al. (Mon,) studied this question.