Decomposition of the total stress energy for the generalized Kiselev black hole

We demonstrate that the anisotropic stress energy supporting the Kiselev black hole can be mimicked by being split into a perfect fluid component plus either an electromagnetic component or a scalar field component, thereby quantifying the precise extent to which the Kiselev black hole fails to represent a perfect fluid spacetime. The perfect fluid component carries either an electric or a scalar charge, which then generates anisotropic electromagnetic or scalar fields. This in turn generates anisotropic contributions to the stress energy. These in turn induce forces that partially (in addition to the fluid pressure gradient) support the matter content against gravity. This decomposition is carried out both for the original one-component Kiselev black hole and for the generalized N-component Kiselev black holes. We also comment on the presence of energy condition violations (specifically for the null energy condition) for certain subclasses of Kiselev black holes.