Vol. 314, No. 1, 2021

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Vanishing conditions on Weyl tensor for Einstein-type manifolds

Benedito Leandro

Vol. 314 (2021), No. 1, 99–113
Abstract

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 $\left(n-1\right)$-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.

Keywords
Einstein-type manifolds, Weyl tensor, harmonic Weyl curvature.
Mathematical Subject Classification 2010
Primary: 53C20, 53C21, 53C25
Milestones
Revised: 1 July 2020
Accepted: 24 July 2021
Published: 15 October 2021
Authors
 Benedito Leandro Universidade Federal de Goiás Goiânia Brazil