Compactly supported instability of Riemannian Schwarzschild--Tangherlini metrics

On the Riemannian Schwarzschild–Tangherlini metric of dimension $n\ge 4$, 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.