  It is common to think of our universe according to the "block universe"
concept, which says that spacetime consists of many "stacked" 3-surfaces,
labelled by some kind of proper time, $\tau$. Standard ideas do not distinguish
past and future, but Ellis "evolving block universe" tries to make a
fundamental distinction. One proposal for this proper time is the proper time
measured along the timelike Ricci eigenlines, starting from the big bang. This
work investigates the shape of the "Ricci time" surfaces relative to the the
null surfaces. We use the Lemaitre-Tolman metric as our inhomogeneous spacetime
model, and we find the necessary and sufficient conditions for these $\{\tau$=
constant$\}$ surfaces, $S(\tau)$, to be spacelike or timelike. Furthermore, we
look at the effect of strong gravity domains by determining the location of
timelike $S$ regions relative to apparent horizons. We find that constant Ricci
time surfaces are always spacelike near the big bang, while at late times (near
the crunch or the extreme far future), they are only timelike under special
circumstances. At intermediate times, timelike $S$ regions are common unless
the variation of the bang time is restricted. The regions where these surfaces
become timelike are often adjacent to apparent horizons, but always outside
them, and in particular timelike $S$ regions do not occur inside black holes.
