Energy conditions in standard static spacetimes |
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Authors: | Dean Allison |
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Institution: | (1) Department of Mathematics, Southern Illinois University-Carbondale, 62901 Carbondale, Illinois |
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Abstract: | Let (H, h) be a Riemannian manifold and letf H (0, ) be a smooth function. The Lorentzian warped product (a,b)
f
×H, -![infin](/content/gu74655872012536/xxlarge8734.gif) a<b![les](/content/gu74655872012536/xxlarge10877.gif) , 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. |
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Keywords: | |
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