The Kiselev black hole is neither perfect fluid, nor is it quintessence
  The Kiselev black hole spacetime, \[ ds^2 = - \left(1-{2m\over r} - {K\over
r^{1+3w}} \right) dt^2 + {dr^2\over1-{2m\over r} - {K\over r^{1+3w}}} + r^2
\,d\Omega_2^2, \] is an extremely popular toy model, with over 200 direct and
indirect citations as of 2019. Unfortunately, despite repeated assertions to
the contrary, this is not a perfect fluid spacetime. The relative pressure
anisotropy and average pressure are easily calculated to satisfy \[ \Delta =
{\Delta p\over \bar p} = {p_r - p_t \over {1\over3} (p_r+2p_t)} =- {3(1+w)\over
2 w}; \qquad\qquad {\bar p\over \rho} = {{1\over3} (p_r + 2p_t)\over \rho} = w.
\] 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 terminology
which has (with very limited exceptions) been copied into the subsequent
literature. Perhaps worse, Kiselev's use of the word "quintessence" does not
match the standard usage in the cosmology community, leading to another level
of unfortunate and unnecessary confusion. Very few of the subsequent follow-up
papers get these points right, so a brief explicit comment is warranted.
