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Curvature Estimates in Asymptotically Flat Lorentzian Manifolds

Published online by Cambridge University Press:  20 November 2018

Felix Finster  and
Margarita Kraus
Felix Finster
Affiliation:
Naturwissenschaftliche Fakultät I – Mathematik, Universität Regensburg, D-93040 Regensburg, Germany, e-mail: felix.finster@mathematik.uni-regensburg.de, e-mail: margarita.kraus@mathematik.uni-regensburg.de
Margarita Kraus
Affiliation:
Naturwissenschaftliche Fakultät I – Mathematik, Universität Regensburg, D-93040 Regensburg, Germany, e-mail: felix.finster@mathematik.uni-regensburg.de, e-mail: margarita.kraus@mathematik.uni-regensburg.de
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Abstract

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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 $\text{ADM}$ 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 $\text{ADM}$ energy tends to zero.

Keywords

53C2153C2783C57
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 4 , 01 August 2005 , pp. 708 - 723
Copyright
Copyright © Canadian Mathematical Society 2005

References

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