The Kiselev solution in power-Maxwell electrodynamics

TL;DR

This paper demonstrates that the Kiselev black hole solution can be derived from power-Maxwell nonlinear electrodynamics, providing a new physical interpretation and analyzing thermodynamic properties including heat capacity and potential as a heat engine.

Contribution

It establishes the Kiselev geometry as an exact solution of Einstein equations coupled with power-Maxwell electrodynamics, linking it to specific nonlinear electromagnetic sources.

Findings

Kiselev geometry is an exact solution in power-Maxwell electrodynamics.

Charged particle motion analyzed in this geometry.

Black hole thermodynamics shows Schottky peaks, indicating heat engine potential.

Abstract

In this work we reconsider the solution describing black holes surrounded by a `quintessence'-like fluid. This geometry was introduced by Kiselev in 2003 and its physical source was originally modeled by an anisotropic fluid. We show that the Kiselev geometry is actually an exact solution of the Einstein equations coupled to nonlinear electrodynamics. More specifically, we show that the Kiselev geometry becomes an exact solution in the context of power-Maxwell electrodynamics, using either an electric ansatz or a magnetic one. In both cases the physical source can be modeled by a power-Maxwell Lagrangian, albeit with different powers corresponding to the electric or the magnetic charges. We briefly investigate the motion of charged particles in this geometry. Finally, we give the proper interpretation of the black-hole thermodynamics in this context. Similarly to the Schwarzschild-de Sitter case, we note the presence of the Schottky peaks in the heat capacity, signaling out the possibility of this thermodynamic black hole system to function as a continuous heat machine.