Counterexamples to a divergence lower bound for the covariant derivative of skew-symmetric 2-tensor fields

Counterexamples to a divergence lower bound for the covariant derivative of skew-symmetric 2-tensor fields

Ann Glob Anal Geom 63, 18 (2023) In arXiv:2103.15482 an estimate for suitable skew-symmetric 2-tensors was claimed. Soon after, this estimate has been exploited to claim powerful classification results: most notably, it has been employed to propose a proof of a Black Hole Uniqueness Theorem for vacu...

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Bibliographic Details
Main Authors: Borghini, Stefano, Mazzieri, Lorenzo
Format: Journal Article
Language:English
Published: 06-01-2023
Subjects:
Mathematics - Differential Geometry
Physics - General Relativity and Quantum Cosmology
Online Access:Get full text
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Summary:Ann Glob Anal Geom 63, 18 (2023) In arXiv:2103.15482 an estimate for suitable skew-symmetric 2-tensors was claimed. Soon after, this estimate has been exploited to claim powerful classification results: most notably, it has been employed to propose a proof of a Black Hole Uniqueness Theorem for vacuum static spacetimes with positive scalar curvature and in connection with the Besse Conjecture. In the present note we point out an issue in the argument proposed in arXiv:2103.15482 and we provide a counterexample to the estimate.
DOI:10.48550/arxiv.2301.02633