Implications of energy conditions on standard static space–times

Abstract

In the framework of standard static space times, we state a family of sufficient or necessary conditions for a set of physically reasonable energy and convergence conditions in relativity and related theories. We concentrate our study on questions about the sub-harmonicity of the warping function, the scalar curvature map, conformal hyperbolicity, conjugate points and the time-like diameter of this class of space-times.

Geometry of Twisted Products and Applications on Static Perfect Fluid Spacetimes

“…If ∆φ = − τ n−1 φ holds in (5.1), then it turns into φRic − h φ = −(∆φ)g, (5.8) which is the equation of vacuum static space. Therefore, static perfect fluid spacetimes behave like a generalization of static vacuum spaces which are an important subject of study in both differential geometry and general relativity, [13]. From Theorem 5.1, we finally have:…”