  A large number of binary black holes (BBHs) with longer orbital periods are
supposed to exist as progenitors of BBH mergers recently discovered with
gravitational wave (GW) detectors. In our previous papers, we proposed to
search for such BBHs in triple systems through the radial-velocity modulation
of the tertiary orbiting star. If the tertiary is a pulsar, high precision and
cadence observations of its arrival time enable an unambiguous characterization
of the pulsar -- BBH triples located at several kpc, which are inaccessible
with the radial velocity of stars. The present paper shows that such inner BBHs
can be identified through the short-term R{\o}mer delay modulation, on the
order of $10$ msec for our fiducial case, a triple consisting of $20~M_\odot$
BBH and $1.4~M_\odot$ pulsar with $P_\mathrm{in}=10$ days and
$P_\mathrm{out}=100$ days. If the relativistic time delays are measured as
well, one can determine basically all the orbital parameters of the triple. For
instance, this method is applicable to inner BBHs of down to $\sim 1$ hr
orbital periods if the orbital period of the tertiary pulsar is around several
days. Inner BBHs with $\lesssim 1$ hr orbital period emit the GW detectable by
future space-based GW missions including LISA, DECIGO, and BBO, and very short
inner BBHs with sub-second orbital period can be even probed by the existing
ground-based GW detectors. Therefore, our proposed methodology provides a
complementary technique to search for inner BBHs in triples, if exist at all,
in the near future.
