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This article is available for purchase or by subscription. See below.
Abstract
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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.
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Keywords
Einstein-type manifolds, Weyl tensor, harmonic Weyl
curvature.
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Mathematical Subject Classification 2010
Primary: 53C20, 53C21, 53C25
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Milestones
Received: 11 June 2019
Revised: 1 July 2020
Accepted: 24 July 2021
Published: 15 October 2021
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