Counterexamples to a divergence lower bound for the covariant derivative of skew-symmetric 2-tensor fields
Differential Geometry
2023-03-23 v1 General Relativity and Quantum Cosmology
Abstract
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.
Keywords
Cite
@article{arxiv.2301.02633,
title = {Counterexamples to a divergence lower bound for the covariant derivative of skew-symmetric 2-tensor fields},
author = {Stefano Borghini and Lorenzo Mazzieri},
journal= {arXiv preprint arXiv:2301.02633},
year = {2023}
}
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8 pages