  Shock wave reflection from a rigid wall has been thoroughly studied in the
Newtonian limit, simplifying the problem by analyzing it in a steady-state
frame, $S'$, where the point $P$ of the shock's intersection with the wall is
at rest. However, a "super-luminal" regime emerges when the velocity of point
$P$ ($v_p$) exceeds the speed of light ($v_p>c$), where no steady-state frame
$S'$ exists. It occurs predominantly in the relativistic regime, relevant in
astrophysics, where it encompasses nearly all of the shock incidence angles. To
study this regime, we introduce a new approach. We formulate integral
conservation laws in the lab frame $S$ (where the unshocked fluid is at rest)
for regular reflection (RR), using two methods: a. fixed volume analysis and b.
fixed fluid analysis. We show the equivalence between the two methods, and also
to the steady-state oblique shock jump conditions in frame $S'$ in the
sub-luminal regime ($v_p<c$). Applying this framework, we find that both the
weak and strong shock RR solutions are bounded in the parameter space by the
detachment line on the higher incidence angles side. The strong shock solution
is also bounded by the luminal line on the lower incidence angles side, and
exists only between these two critical lines, in the sub-luminal attachment
region.
