Energy conditions in standard static spacetimes.
Abstract
Let (H, h) be a Riemannian manifold and letf∶H→(0,∞) be a smooth function. The Lorentzian warped product (a,b)_{ f }×H, ∞⩽a<b⩽∞, with metricds ^{2}=(f ^{2} dt ^{2})⊕h is called a standard static spacetime. We investigate conditions on the warping functionf which guarantee that a standard static spacetime (a,b)_{ f }×H satisfies certain of the energy conditions from general relativity. Also, if (H, h) is a complete, finite volume Riemannian manifold with nonpositive Ricci curvature and the gradient off never vanishes onH, then (a, b)_{ f }×H cannot satisfy the null convergence condition.
 Publication:

General Relativity and Gravitation
 Pub Date:
 February 1988
 DOI:
 10.1007/BF00759321
 Bibcode:
 1988GReGr..20..115A
 Keywords:

 General Relativity