Dynamics of energy extraction near a rotating Kiselev black hole

In this 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.