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

TL;DR

This paper proves a positive mass theorem for asymptotically flat graphs in Einstein-Gauss-Bonnet theory, establishing conditions under which the mass is non-negative and deriving a Penrose inequality for positive coupling.

Contribution

It introduces a positive mass theorem in Einstein-Gauss-Bonnet theory for asymptotically flat graphs under a specific curvature condition, extending previous results.

Findings

Positive mass theorem for asymptotically flat graphs.

Non-negativity of mass under curvature condition R + αL_2 ≥ 0.

Penrose inequality for α > 0 case.

Abstract

As an interesting application of the Einstein-Gauss-Bonnet theory and our work on the Gauss-Bonnet-Chern mass (Ge, Wang, Wu), we obtain a positive mass theorem for asymptotically flat graphs in $\R^{n+1}$ under a condition that $R+\alpha L_2$ is non-negative, where $R$ is the scalar curvature, $\alpha\in\R$ a constant and $L_2$ the second Gauss-Bonnet curvature. A Penrose type inequality is also obtained in the case $\alpha>0$.