Greybody factor for accelerating rotating BTZ black hole

Abstract 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, $$\Gamma (\omega ) \propto (\omega - m \Omega _H)^{2\lambda - 1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Γ</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>-</mml:mo> <mml:mi>m</mml:mi> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mi>H</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>λ</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , where $$\lambda = \sqrt{\mu ^2 \ell ^2 + 5/4}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:msqrt> <mml:mrow> <mml:msup> <mml:mi>μ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>+</mml:mo> <mml:mn>5</mml:mn> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msqrt> </mml:mrow> </mml:math> , highlighting deviations from pure blackbody radiation. We discuss implications for Hawking radiation, superradiance in the regime $$\omega &lt; m \Omega _H$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mi>m</mml:mi> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mi>H</mml:mi> </mml:msub> </mml:mrow> </mml:math> , and the role of acceleration in modifying black hole thermodynamics.