Gravitational lensing by $p$-branes

The scattering of R-R gauge bosons off of Dirichlet $p$-branes is computed to leading order in the string coupling. The results are qualitatively similar to those found in the scattering of massless NS-NS bosons: all $p$-branes with $p\geq 0$ exhibit stringy properties, in particular the Regge behavior. Both the R-R and NS-NS scattering amplitudes agree in the limit of small momentum transfer with scattering off the extremal R-R charged $p$-brane solutions found in the low-energy supergravities. We interpret this as evidence that Dirichlet-branes are an exact world-sheet description of the extremal $p$-branes. The $-1$-brane (D-instanton) is a special object which, unlike all other Dirichlet-branes, exhibits point-like behavior. We find the R-R charged instanton solution to type~IIB supergravity and confirm that the field theoretic scattering off of this solution miraculously reproduces the full stringy calculation. As an aside, we include a discussion of the entropy of non-extremal black holes in ten dimensions, produced by exciting the $0$-brane. We show that, for large black holes, the entropy grows linearly with the black hole mass.