The gravitational wave observed on September 14, 2015 was because of the merger of two black holes of mass 36 and 29 times that of our Sun. According to Newtonian theory, black holes orbiting around each other will follow circular or an elliptical orbit. Einstein maintained that they would spiral inwards towards each other (the inspiral phases) and when they are close would form a circular orbit and then in a jiffy, they'd unite (merger and ringdown phase). The energy dissipated in this process could form gravitational waves which will bear the signature of the inspiral, merger and ringdown phases.
General Theory of Relativity has been tested at low speeds, in other words, approximately in the order of 0.001 times the speed of light. However, the above phenomena was the only one when it is tested at high speed. And, it is proved right on many counts.
First, the spin and mass of the merged mass fit with what was calculated using the signal obtained during the merger and ringdown phases.
Second, during the inspiral phase, when the black holes are far apart, they were moving at about 0.1-0.4 times the speed of light. At this comparatively low speed, the system can be treated as a correction, to the Newtonian description. According to the Newton's theory, the black holes are supposed to orbit each other in a circular or elliptical orbit and there will be no loss of energy by means of gravitational waves which makes them fall inwards. In reality correction factors obtained using Newtonian dynamics was of higher order. Using this approach, and using so-called post-Newtonian coefficients, they are found to fit with what has been inferred from experimentally detected signal.
Lastly, as pointed out in the General Theory of Relativity, gravitational waves must be "dispersionless" that is, the field particle associated with gravitation should have a zero mass. This implied that all the wavelength components of the wave should travel in the same speed. This was also verified in the form of the wave.
'The famous "chirp" that was heard proves the dispersionless character of the component waves. Dispersion would have introduced a change in the characteristic in the signal that was observed. A strong dispersion, would have introduced an "inverted chirp"', said Dr. P. Ajith of the International Centre for Theoretical Sciences, Bengaluru.