  We study scattering on the black hole horizon in a partial wave basis, with
an impact parameter of the order of the Schwarzschild radius or less. This
resembles the strong gravity regime where quantum gravitational effects appear.
The scattering is governed by an infinite number of virtual gravitons exchanged
on the horizon. Remarkably, they can all be summed non-perturbatively in
$\hbar$ and $\gamma \sim M_{Pl}/M_{BH}$. These results generalise those
obtained from studying gravitational backreaction. Unlike in the eikonal
calculations in flat space, the relevant centre of mass energy of the
collisions is not necessarily Planckian; instead it is easily satisfied, $s \gg
\gamma^2 M^2_{Pl}$, for semi-classical black holes. The calculation lends
further support to the scattering matrix approach to quantum black holes, and
is a second-quantised generalisation of the same.
