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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: [email protected], e-mail: [email protected]
Margarita Kraus
Affiliation:
Naturwissenschaftliche Fakultät I – Mathematik, Universität Regensburg, D-93040 Regensburg, Germany, e-mail: [email protected], e-mail: [email protected]
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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

[1] Arnowitt, R., Deser, S., and Misner, C., Energy and the criteria for radiation in general relativity. Phys. Rev. 118(1960), 1100–1104.Google Scholar
[2] Bartnik, R., The mass of an asymptotically flat manifold. Commun. Pure Appl. Math. 39(1986), 661–693.Google Scholar
[3] Baum, H., Spin-Strukturen und Dirac-Operatoren über pseudo-Riemannschen Mannigfaltigkeiten. Teubner-Texte zurMathematik 41, Teubner Verlag, Leipzig, 1981.Google Scholar
[4] Bray, H. and Finster, F., Curvature estimates and the positive mass theorem. Comm. Anal. Geom. 10(2002), 291–306.Google Scholar
[5] Finster, F. and Kath, I., Curvature estimates in asymptotically flat manifolds of positive scalar curvature. Comm. Anal. Geom. 10(2002), 1017–1031.Google Scholar
[6] Lawson, H. B. and Michelsohn, M.-L., Spin Geometry, PrincetonMathematical Series 38, Princeton University Press, Princeton, NJ, 1989.Google Scholar
[7] Schoen, R. and Yau, S. T., On the proof of the positive mass conjecture in general relativity. Commun. Math. Phys. 65(1979), 45–76.Google Scholar
[8] Parker, T. and Taubes, C. H., On Witten's proof of the positive energy theorem. Commun.Math. Phys. 84(1982), 223–238.Google Scholar
[9] Witten, E., A new proof of the positive energy theorem. Commun. Math. Phys. 80(1981), 381–402.Google Scholar