Curvature Estimates in Asymptotically Flat Lorentzian Manifolds

Details Curvature Estimates in Asymptotically Flat Lorentzian Manifolds Curvature Estimates in Asymptotically Flat Lorentzian Manifolds

2003-06-10

arxiv.org/abs/math/0306159v2

Canad. J. Math. 57 (2005) 708-723

Mathematics

Differential Geometry

15 pages (published version)

Scientific paper

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.

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