The Final State: the fate of relativistic compact objects after merger

We worked on probing the nature of the final relativistic compact object after
the binary merger via gravitational waves. This includes testing the black hole
description given by the general relativity and obtaining the equation of state
of a neutron star. A variety of alternative objects beyond the general relativity
have been proposed such as wormholes, boson stars,
which give different gravitational wave signatures, especially
gravitational wave echoes. The nature of the final excited black hole resulted
from a binary black hole merger can be examined model-dependently by showing
that any additional deviation parameters governing the waveforms are consistent
with zero. We showed that the no-hair conjecture can be tested observationally
with just a few plausible signals detected by the LIGO-Virgo detector network
operating at its design sensitivity. If we have no any prior knowledge about the
waveform, we can make use of the morphology-independent algorithm which can
detect any waveform by comparing the Bayesian evidences among signal, glitch
and noise hypotheses.
We applied the methods to the detected signals of the first gravitational wave
transient catalog and did not find any evidence for echoes. Finally, in the future,
binary neutron star postmergers are expected to be seen with third generation of
gravitational wave interferometers but yet the postmerger waveforms are poorly
known. We discovered new quasi-universal relations and improved existing ones,
which serve as a building block for modelling the postmerger, and demonstrated
the possibility of performing inspiral-merger-postmerger consistency tests.