Vanishing conditions on Weyl tensor for Einstein-type manifolds
Differential Geometry
2021-10-27 v6
Abstract
In this paper we consider an Einstein-type equation which generalizes important geometric equations, like static and critical point equations. We prove that a complete Einstein-type manifold with fourth-order divergence-free Weyl tensor and zero radial Weyl curvature is locally a warped product with -dimensional Einstein fibers, provided that the potential function is proper. As a consequence, we prove a result about the nonexistence of multiple black holes in static spacetimes.
Cite
@article{arxiv.1904.12384,
title = {Vanishing conditions on Weyl tensor for Einstein-type manifolds},
author = {Benedito Leandro},
journal= {arXiv preprint arXiv:1904.12384},
year = {2021}
}