Decoupling of gravity on non-susy D$p$ branes

We study the graviton scattering in the background of non-susy D$p$ branes of type II string theories consisting of a metric, a dilaton and a $(p+1)$ form gauge field. We show numerically that in these backgrounds graviton experiences a scattering potential which takes the form of an infinite barrier in the low energy (near brane) limit for $p\leq 5$ and therefore is never able to reach the branes. This shows, contrary to what is known in the literature, that gravity indeed decouples from the non-susy D$p$ branes for $p \leq 5$. For non-susy D6 brane, gravity couples as there is no such barrier for the potential. To give further credence to our claim we solve the scattering equation in some situation analytically and calculate the graviton absorption cross-sections on the non-susy branes and show that they vanish for $p \leq 4$ in the low energy limit. This shows, as in the case of BPS branes, that gravity does decouple for non-susy D$p$ branes for $p\leq 4$ but it does not decouple for D6 brane as the potential here is always attractive. We argue for the non-susy D5 brane that depending on one of the parameters of the solution gravity either always decouples (unlike the BPS D5 brane) or it decouples when the energy of the graviton is below certain critical value, otherwise it couples, very similar to BPS D5 brane.