Greybody factor for accelerating rotating BTZ black hole

We investigate the greybody factor for the accelerating rotating Bañados–Teitelboim–Zanelli (BTZ) black hole in (2+1)-dimensional spacetime. Due to the non-separability of the Klein–Gordon equation induced by the acceleration parameter, we employ an azimuthal-average approximation to derive an effective potential for massless scalar fields. In the low-frequency limit, we solve the radial equation using matched asymptotic expansions near the horizon and in the far region, accounting for rotation via the horizon angular velocity. Our results yield a power-law scaling for the greybody factor, Γ (ω ) ∝ (ω - m Ω H)2λ - 1 Γ ( ω ) ∝ ( ω - m Ω H ) 2 λ - 1 , where λ = √μ ² ² + 5/4 λ = μ 2 ℓ 2 + 5 / 4 , highlighting deviations from pure blackbody radiation. We discuss implications for Hawking radiation, superradiance in the regime ω < m Ω H ω < m Ω H , and the role of acceleration in modifying black hole thermodynamics.