The Kiselev black hole spacetime , ds ^ { 2 } = - \left ( 1 - { 2 m \over r } - { K \over r ^ { 1 + 3 w } } \right ) dt ^ { 2 } + { dr ^ { 2 } \over 1 - { 2 m% \over r } - { K \over r ^ { 1 + 3 w } } } + 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 \over 3 } ( p _ { r } +2 p _ { t } ) } = - { 3 ( 1 % + w ) \over 2 w } ; { \bar { p } \over \rho } = { { 1 \over 3 } ( p _ { r } +2 p _ { 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 . Date : 29 August 2019 ; LaTeX-ed August 27 , 2020 Keywords : Kiselev black hole ; perfect fluids ; quintessence . PhySH : Gravitation ; Classical black holes ; Fluids & classical fields in curved spacetime .