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arXiv · 1904.12384

Vanishing conditions on Weyl tensor for Einstein-type manifolds

Benedito Leandro
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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 $(n-1)$-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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Benedito Leandro. 2019-04-28. Vanishing conditions on Weyl tensor for Einstein-type manifolds. https://doi.org/10.2140/pjm.2021.314.99

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