A new mass for asymptotically flat manifolds

Yuxin Ge; Guofang Wang; Jie Wu

A new mass for asymptotically flat manifolds

Differential Geometry 2013-04-30 v2 General Relativity and Quantum Cosmology

Authors: Yuxin Ge , Guofang Wang , Jie Wu

Abstract

In this paper we introduce a mass for asymptotically flat manifolds by using the Gauss-Bonnet curvature. We first prove that the mass is well-defined and is a geometric invariant, if the Gauss-Bonnet curvature is integrable and the decay order $\tau$ satisfies $\tau > \frac {n-4}{3}.$ Then we show a positive mass theorem for asymptotically flat graphs over ${\mathbb R}^n$ . Moreover we obtain also Penrose type inequalities in this case.

Keywords

general relativity riemannian geometry

Cite

@article{arxiv.1211.3645,
  title  = {A new mass for asymptotically flat manifolds},
  author = {Yuxin Ge and Guofang Wang and Jie Wu},
  journal= {arXiv preprint arXiv:1211.3645},
  year   = {2013}
}

Comments

32 pages. arXiv:1211.7305 was integrated into this new version as an application

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