A new mass for asymptotically flat manifolds

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.

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

References in corpus (3)

• Black Holes in Pure Lovelock Gravities
• On the quasi-linearity of the Einstein- "Gauss-Bonnet" gravity field equations
• On the Positive Mass, Penrose, an ZAS Inequalities in General Dimension

Cited by in corpus (1)

• A positive mass theorem in the Einstein-Gauss-Bonnet theory