Vacuum Static Spaces with Harmonic Curvature

Abstract

In this paper, we classify $n$-dimensional ($n\ge 5$) vacuum static spaces with harmonic curvature, thus extending the $4$-dimensional work by Kim-Shin \cite{KS}. As a consequence, we provide new counterexamples to the Fischer-Marsden conjecture on compact vacuum static spaces.

arXiv admin note: substantial text overlap with arXiv:2101.12681