  We explore how X-ray reverberation around black holes may reveal the presence
of the innermost stable circular orbit (ISCO), predicted by General Relativity,
and probe the dynamics of the plunging region between the ISCO and the event
horizon. Being able to directly detect the presence of the ISCO and probe the
dynamics of material plunging through the event horizon represents a unique
test of general relativity in the strong field regime. X-ray reverberation off
of the accretion disc and material in the plunging region is modelled using
general relativistic ray tracing simulations. X-ray reverberation from the
plunging region has a minimal effect on the time-averaged X-ray spectrum and
the overall lag-energy spectrum, but is manifested in the lag in the highest
frequency Fourier components, above 0.01 c^3 (GM)^-1 (scaled for the mass of
the black hole) in the 2-4keV energy band for a non-spinning black hole or the
1-2keV energy band for a maximally spinning black hole. The plunging region is
distinguished from disc emission not just by the energy shifts characteristic
of plunging orbits, but by the rapid increase in ionisation of material through
the plunging region. Detection requires measurement of time lags to an accuracy
of 20 per cent at these frequencies. Improving accuracy to 12 per cent will
enable constraints to be placed on the dynamics of material in the plunging
region and distinguish plunging orbits from material remaining on stable
circular orbits, confirming the existence of the ISCO, a prime discovery space
for future X-ray missions.
