  We study how by careful monitoring of the presence or absence of tidal
deformability (TD) and tidal-heating (TH) in the inspiral signal of compact
object binaries in ground-based gravitational wave (GW) detectors, one can test
if its components are black holes or not. The former property (TD) is finite
for neutron stars but vanishes for black holes (in general relativity), whereas
the latter is finite for black holes and negligible for neutron stars, and
affects the GW phase evolution of binaries in a distinctly different way. We
introduce waveform parameters that characterize the strength of tidal-heating,
and are zero when there is no horizon. We develop Bayesian methods that use TD
and TH for distinguishing the presence or absence of horizons in a binary. This
is timely owing to several claims that these stellar-mass objects, especially,
with masses heavier than those of neutron stars, may not have a horizon but may
be black hole mimickers or exotic compact objects (ECOs). It is also
astrophysically important to have the tools to test the presence or absence of
horizons in mass-gap binaries and, thereby, help detect the heaviest neutron
star or the lightest black hole. A proper accounting of tidal-heating in binary
waveform models will also be critical for an unbiased measurement of
characteristics of the equation of state of neutron stars in GW observations of
binaries containing them -- or even to probe the existence of ECOs. We show
that purely based on GW waveforms it will not be possible to discern binary
horizons in the mass gap in Advanced LIGO, Virgo and KAGRA detectors unless the
binary is within a few tens of Mpc. However, third generation ground-based
detectors will be able to do so for binaries a few hundred Mpc away.
