Some geometric properties of generalized φ-vacuum static spaces

2025/09/05 by Branca, Letizia, Mastrolia, Paolo, Rigoli, Marco
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.05125

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 assumptions; in particular, we prove a result related to the famous Cosmic no-hair conjecture of Boucher, Gibbons and Horowitz.

Citations

• Geometry of Einstein-type manifolds with boundary
• Geometry of static perfect fluid space-time
• On the volume functional of compact manifolds with boundary with constant scalar curvature
• On Einstein Manifolds of Positive Sectional Curvature

Related

• Vacuum Static Spaces with Harmonic Curvature
• Vacuum static spaces with harmonic curvature
• 3-dimensional complete vacuum static spaces
• Vacuum static spaces with vanishing of complete divergence of Bach tensor and Weyl tensor
• Vacuum Static Spaces with Positive Isotropic Curvature