 |
|
Curvature Estimates in Asymptotically Flat Lorentzian Manifolds |
Canad. J. Math. 57(2005), 708-723
Published:2005-08-01
Printed: Aug 2005
Printed: Aug 2005
- Felix Finster
- Margarita Kraus
Abstract
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.
| MSC Classifications: |
53C21 - Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 53C27 - Spin and Spin$^c$ geometry 83C57 - Black holes |