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# Curvature Estimates in Asymptotically Flat Lorentzian Manifolds

Published:2005-08-01
Printed: Aug 2005
• Felix Finster
• Margarita Kraus
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## Abstract

We consider an asymptotically flat Lorentzian manifold of dimension $(1,3)$. An inequality is derived which bounds the Riemannian curvature tensor in terms of the ADM energy in the general case with second fundamental form. The inequality quantifies in which sense the Lorentzian manifold becomes flat in the limit when the ADM energy tends to zero.
 MSC Classifications: 53C21 - Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 53C27 - Spin and Spin$^c$ geometry 83C57 - Black holes

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