Exploration of the Ergoregion of a Rotating Charged Black Hole in Perfect Fluid Dark Matter

In this work, we use the solutions for a rotating, charged black hole in perfect fluid dark matter obtained by Das et al (Class. Quantum Grav., 2021) to examine the properties of the black hole’s ergoregion. We find that for any combination of values for the charge Q and the spin parameter a of the black hole, there is a range of values of the perfect fluid dark matter (PFDM) parameter α for which the ergoregion exists. We define α_max as the upper limit of α values for which the ergoregion still exists and α_min as the lower limit. We determine that, for any combination of values of Q and a < M, α_max remains at approximately 7.1M. However, holding a constant, α_min increases as Q increases, with α_min ≈ 0.82M when a = M and Q = 0. Similarly, when we hold Q constant and increase a, α_min increases exponentially. Furthermore, when α gets small enough it becomes negligible and the ergoregion returns to that of a rotating charged black hole without the PFDM.