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The Kiselev black hole spacetime, \[ ds^2 = - \left(1-{2m\over r} - {K\overr^{1+3w}} \right) dt^2 + {dr^2\over1-{2m\over r} - {K\over r^{1+3w}}} + r^2\,d\Omega_2^2, \] is an extremely popular toy model, with over 200 direct andindirect citations as of 2019. Unfortunately, despite repeated assertions tothe contrary, this is not a perfect fluid spacetime. The relative pressureanisotropy and average pressure are easily calculated to satisfy \[ \Delta ={\Delta p\over \bar p} = {p_r - p_t \over {1\over3} (p_r+2p_t)} =- {3(1+w)\over2 w}; \qquad\qquad {\bar p\over \rho} = {{1\over3} (p_r + 2p_t)\over \rho} = w.\] The relative pressure anisotropy $\Delta$ is generally a non-zero constant,(unless $w=-1$, corresponding to Schwarzschild-(anti)-de Sitter spacetime).Kiselev's original paper was very careful to point this out in the calculation,but then in the discussion made a somewhat unfortunate choice of terminologywhich has (with very limited exceptions) been copied into the subsequentliterature. Perhaps worse, Kiselev's use of the word "quintessence" does notmatch the standard usage in the cosmology community, leading to another levelof unfortunate and unnecessary confusion. Very few of the subsequent follow-uppapers get these points right, so a brief explicit comment is warranted.

The Kiselev black hole is neither perfect fluid, nor is it quintessence