  Black hole (BH) thermodynamics was established by Bekenstein and Hawking, who
made abstract theoretical arguments about the second law of thermodynamics and
quantum theory in curved spacetime respectively. Testing these ideas
experimentally has, so far, been impractical because the putative flux of
Hawking radiation from astrophysical BHs is too small to be distinguished from
the rest of the hot environment. Here, it is proposed that the spectrum of
emitted gravitational waves (GWs) after the merger of two BHs, in particular
the spectrum of GW150914, can be used to infer a lower limit on the magnitude
of the entropy of the post-merger BH. This lower bound is potentially
significant as it could be of the same order as the Bekenstein-Hawking entropy.
To infer this limit, we first assume that the result of the merger is an
ultracompact object with an external geometry which is Schwarzschild or Kerr,
but with an outer surface which is capable of reflecting in-falling GWs rather
than fully absorbing them. If the absence of deviations from the predictions of
general relativity in detected GW signals will be verified, we will then obtain
a bound on the minimal redshift factor of GWs that emerge from the vicinity of
the object's surface. This lack of deviations would also mean that the remnant
of the merger has to have a strongly absorbing surface and must then be a BH
for all practical purposes. We conclude that a relationship between the minimal
redshift factor and the BH entropy, which was first proposed by 't Hooft, could
then be used to set a lower bound on the entropy of the post-merger BH.
