Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-19T22:12:26.261Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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