Boosts, Schwarzschild black holes and absorption cross sections in M-theory

D-dimensional neutral black strings wrapped on a circle are related to (D - 1)-dimensional charged black holes by boosts. We show that the boost has to be performed in the covering space and the boosted coordinate has to be compactified on a circle with a Lorentz contracted radius. Using this fact we show that the transition between Schwarzschild black holes to black p-branes observed recently in M-theory is the well-known black hole-black string transition viewed in a boosted frame. In a similar way the correspondence point where an excited string state goes over to a neutral black hole is mapped exactly to the correspondence point for black p-branes. In terms of the p-brane quantities, the equation of state for an excited string state becomes identical to that of a (3 + 1)-dimensional massless gas for all p. Finally, we show how boosts can be used to relate Hawking radiation rates. Using the known microscopic derivation of absorption by extremal 3-branes and near-extremal 5D holes with three large charges we provide a microscopic derivation of absorption of 0-branes by seven- and five-dimensional Schwarzschild black holes in a certain regime.