Decomposition of total stress-energy for the generalised Kiselev black hole

TL;DR

This paper decomposes the stress-energy tensor of the generalized Kiselev black hole into perfect fluid and electromagnetic or scalar field components, clarifying the sources of anisotropy and energy condition violations.

Contribution

It introduces a method to split the anisotropic stress-energy of Kiselev black holes into simpler components, extending to N-component cases and analyzing energy condition violations.

Findings

Decomposition into perfect fluid plus electromagnetic or scalar fields.

Identification of energy condition violations in certain subclasses.

Extension of the decomposition method to generalized N-component Kiselev black holes.

Abstract

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 which partially (in addition to the fluid pressure gradient) support the matter content against gravity. This decomposition is carried out both for the original 1-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 --- NEC) for certain sub-classes of Kiselev black holes.