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

We study the 5D black holes in the type IIB superstring theory compactified on $S^1 \times T^4$. Far from horizon, we have flat space-time. Near horizon, we have $AdS_3({\rm BTZ black hole}) \times S^3 \times T^4$. We calculate the greybody factor of a minimally coupled scalar by replacing the original geometry($M_5 \times S^1 \times T^4$) by $AdS_3 \times S^3 \times T^4$ near horizon, with a flat space-time at spatial infinity. In the 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($AdS_3 \times S^3 \times T^4$) contains the essential information about the bulk 5D black holes.