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:
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- General Relativity