Some geometric properties of generalized $\phi$-vacuum static spaces

Abstract

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