Curvature Estimates in Asymptotically Flat Lorentzian Manifolds

Finster, Felix ; Kraus, Margarita

Canadian journal of mathematics, Tome 57 (2005) no. 4, pp. 708-723

Résumé

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.

Détail

DOI : 10.4153/CJM-2005-028-6

Mots-clés : 53C21, 53C27, 83C57

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