A Novel Kerr-like Black Hole in a General Double Power Law Dark Matter Environment: Geometry, Spectroscopy, and Energy Extraction

Abstract: We construct a novel Kerr-like black hole solution embedded in a general double power law dark matter environment by applying the Newman--Janis algorithm to a Schwarzschild-like seed geometry. This framework provides a unified rotating spacetime for arbitrary double power law density profiles and reveals how dark matter modifies the horizon structure, extremal spin, and curvature properties of rotating black holes. Remarkably, we find that the rotation--halo interplay can eliminate essential curvature singularities for Dehnen-type profiles with $γ\leq2$, despite the singular nature of the corresponding static configurations. We then investigate the spectroscopic signatures of the dark matter environment through massive scalar perturbations in the Dehnen $(1,4,γ)$ halo. Using an analytical low-frequency matching method, we derive the quasibound state spectrum, the onset condition for scalar cloud formation, and superradiant amplification factor, showing that the halo parameters $ρ_0 r_0<sup>3$ and $γ$ leave characteristic imprints on the scalar spectrum. Increasing the halo density or the cusp strengthens the binding of quasibound states and enhances their decay, shifts the scalar cloud threshold, and suppresses superradiant amplification effectivity by narrowing the allowed frequency window and lowering the amplification factor peak. Finally, we analyze rotational energy extraction from thermal scalar fields and demonstrate that the efficiency is controlled by the interplay between the thermal spectrum and the superradiant instability, with lower temperatures and less cuspy density profiles yielding more efficient energy extraction.