  We study the Cauchy Problem for the relativistic Boltzmann equation with near
Vacuum initial data. Unique global in time "mild" solutions are obtained
uniformly in the speed of light parameter $c \ge 1$. We furthermore prove that
solutions to the relativistic Boltzmann equation converge to solutions of the
Newtonian Boltzmann equation in the limit as $c\to\infty$ on arbitrary time
intervals $[0,T]$, with convergence rate $1/c^{2-\epsilon}$ for any $\epsilon
\in(0,2)$. This may be the first proof of unique global in time validity of the
Newtonian limit for a Kinetic equation.
