Holographic connection between the BTZ black hole and 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, 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 $AdS$-boundary theory ($AdS_3 \times S^3 \times T^4$), like a hologram, contains the essential information about the bulk 5D black holes.