Implications of Energy Conditions on Standard Static Space-times

TL;DR

This paper explores how energy conditions influence the geometric and causal properties of standard static space-times, providing conditions related to curvature, hyperbolicity, and conjugate points.

Contribution

It establishes new necessary and sufficient conditions linking energy conditions to geometric features in static space-times.

Findings

Conditions for sub-harmonicity of the warping function

Relations between energy conditions and conjugate points

Implications for the time-like diameter of 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.