Dynamics of Energy Extraction Near a Rotating Kiselev Black Hole

In the current work, we explore the dynamics of energy extraction in the spacetime of a rotating Kiselev black hole, where the central black hole is surrounded by matter fields described by different equations of state: dust ([Formula: see text]), radiation ([Formula: see text]), and quintessence-like dark energy ([Formula: see text]). We analyze how black hole spin [Formula: see text], modified gravity parameter [Formula: see text], and matter intensity [Formula: see text] affect the existence of horizons, ergoregion size, particle angular velocities, and energy extraction mechanisms. Our results reveal that both the Penrose process efficiency and the Blandford-Znajek jet power are significantly influenced by the interplay between these parameters. In particular, the highest energetic outputs are achieved for rapidly rotating black holes in the presence of quintessence-like fields and lower matter intensity. These findings demonstrate that the surrounding environment and gravity modifications play a critical role in black hole energetics and offer potential observational signatures for testing deviations from general relativity.