  In this paper, sharp two-sided estimates for the transition densities of
relativistic $\alpha$-stable processes with mass $m\in (0, 1]$ in $C^{1,1}$
exterior open sets are established for all time $t>0$. These transition
densities are also the Dirichlet heat kernels of
$m-(m^{2/\alpha}-\Delta)^{\alpha/2}$ with $m\in (0, 1]$ in $C^{1,1}$ exterior
open sets. The estimates are uniform in $m$ in the sense that the constants are
independent of $m\in (0, 1]$. As a corollary of our main result, we establish
sharp two-sided Green function estimates for relativistic $\alpha$-stable
processes with mass $m\in (0, 1]$ in $C^{1,1}$ exterior open sets.

Probability