Could we recognize a pure relativistic black hole from gravitational wave signals?

Black holes are extremely simple astrophysical objects that arise from the mathematical theory of general relativity. Although the recent detections of gravitational waves have made us more confident about the existence of black-hole-like objects, further observations are needed to exclude other more exotic objects. The method presented in this talk to address the issue of how the observed objects are related to real black-hole objects, is based on the distinct dynamics followed by integrable systems such us the ones describing the orbits around black holes.