Massive spin 2 excitations in $AdS_6\times S^2$ warped spacetimes

We study (massive) spin-2 fluctuations around warped $AdS_6$ solutions with $16$ supersymmetries in type IIB supergravity. We identify two classes of fluctuations which are universally present for all solutions of this form. The holographically dual operators have scaling dimensions $\Delta=5+3\ell$ and $\Delta=6+3\ell$, where the integer $\ell$ encodes the $R$-symmetry charge. They are identified as descendant states in respective BPS multiplets (the current multiplet for $\Delta=5$). We also compute the normalization of the energy-momentum tensor two-point function and show that it is related to the $S^5$ partition function of the dual $5d$ SCFTs.