  The defining feature of a classical black hole is being a perfect absorber.
Any evidence showing otherwise would indicate a departure from the standard
black-hole picture. Energy and angular momentum absorption by the horizon of a
black hole is responsible for tidal heating in a binary. This effect is
particularly important in the latest stages of an extreme mass ratio inspiral
around a spinning supermassive object, one of the main targets of the future
LISA mission. We study how this effect can be used to probe the nature of
supermassive objects in a model independent way. We compute the orbital
dephasing and the gravitational-wave signal emitted by a point particle in
circular, equatorial motion around a spinning supermassive object to the
leading order in the mass ratio. Absence of absorption by the central object
can affect the gravitational-wave signal dramatically, especially at high spin.
This effect will make it possible to put an unparalleled upper bound on the
reflectivity of exotic compact objects, at the level of ${\cal O}(0.01)\%$.
This stringent bound would exclude the possibility of observing echoes in the
ringdown of a supermassive binary merger.
