  In this paper, we study the asymptotic behavior, as the time $t$ goes to
zero, of the trace of the semigroup of a killed relativistic $\alpha$-stable
process in bounded $C^{1,1}$ open sets and bounded Lipschitz open sets. More
precisely, we establish the asymptotic expansion in terms of $t$ of the trace
with an error bound of order $t^{2/\alpha}t^{-d/\alpha}$ for $C^{1,1}$ open
sets and of order $t^{1/\alpha}t^{-d/\alpha}$ for Lipschitz open sets. Compared
with the corresponding expansions for stable processes, there are more terms
between the orders $t^{-d/\alpha}$ and $t^{(2-d)/\alpha}$ for $C^{1,1}$ open
sets, and, when $\alpha\in (0, 1]$, between the orders $t^{-d/\alpha}$ and
$t^{(1-d)/\alpha}$ for Lipschitz open sets.
