Greybody factor for the BTZ black hole and a 5D black hole

We study 5D black holes in type IIB superstring theory compactified on $S^1\times T^4.$ Far from the horizon, we have flat space-time. Near the horizon, we have ${\mathrm{AdS}}_3\hspace{0.5em}\left(\mathrm{BTZ}\mathrm{}\mathrm{black}\mathrm{}\mathrm{hole}\right)\times S^3\times T^4.$ We calculate the greybody factor of a minimally coupled scalar by replacing the original geometry ${(M}_5\times S^1\times T^4)$ by ${\mathrm{AdS}}_3\times S^3\times T^4.$ In low-energy scattering, it turns out that the result agrees with the greybody factor of the 5D black hole (or D1 + D5 branes) in the dilute gas approximation. This confirms that the AdS theory $({\mathrm{AdS}}_3\times S^3\times T^4)$ contains the essential information about bulk 5D black holes.