PreprintCC BY 4.0HAL
Compactly supported instability of Riemannian Schwarzschild–Tangherlini metrics
Abstract
On the Riemannian Schwarzschild--Tangherlini metric of dimension n≥ 4, we show that the destabilizing TT tensor of Ozuch lies in the image of the ``TT-tensor machine''. By continuity, it can then be approximated, in suitable weighted Sobolev spaces, by smooth compactly supported TT tensors, on which the stability quadratic form is still negative. This proves instability in the usual sense for noncompact manifolds. To our knowledge, no exact smooth compactly supported destabilizing TT tensor was known before, even in 4D.
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BibTeX
@misc{delay2026compactly,
title = {{Compactly supported instability of Riemannian Schwarzschild–Tangherlini metrics}},
author = {Erwann Delay},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13507},
eprint = {2610.13507},
archivePrefix = {arXiv},
url = {https://univ-avignon.hal.science/hal-05788340v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Compactly supported instability of Riemannian Schwarzschild–Tangherlini metrics
AU - Erwann Delay
PY - 2026
DA - 2026/10/09
PB - HAL
DO - 10.48550/arxiv.2610.13507
UR - https://univ-avignon.hal.science/hal-05788340v1
AB - On the Riemannian Schwarzschild--Tangherlini metric of dimension n≥ 4, we show that the destabilizing TT tensor of Ozuch lies in the image of the ``TT-tensor machine''. By continuity, it can then be approximated, in suitable weighted Sobolev spaces, by smooth compactly supported TT tensors, on which the stability quadratic form is still negative. This proves instability in the usual sense for noncompact manifolds. To our knowledge, no exact smooth compactly supported destabilizing TT tensor was known before, even in 4D.
ER -