After the much-discussed, many-author paper in Physical Review Letters revealed the detection of a gravitational wave (denoted GW150914), the LIGO Scientific Collaboration is submitting another paper on how the characteristics of the signal detected vouch for Einstein’s general theory of relativity.
The gravitational wave detected on September 14, 2015 was due to the merger of two black holes of mass 36 and 29 times the mass of our Sun. According to Newtonian dynamics, if the black holes had been orbiting around each other, they would have been in a circular or an elliptical orbit. Einstein however said that they would spiral inwards towards each other (the inspiral phases) and when they came close would lock in a circular orbit, where, in a jiffy, they would merge (merger and ringdown phase). The energy lost in this process would be emitted as gravitational waves which bore the signature of the inspiral, merger and ringdown stages.
There have been many tests of General Theory of Relativity at low speeds, that is, in the order of 0.001 times the speed of light. The specialty of GW150914 was that it was emitted due to a high-speed event, the black hole merger described above.
Here are a few of the ways in which it was shown that the equations of General Theory of Relativity stood the test at the high speeds: first, the spin and mass of the merged entity, as predicted by the part of the signal representing the inspiral phase, matched with what was calculated using the part of the signal representing the merger and ringdown phases.
Second, during the inspiral phase, when the black holes are far apart, they are moving at about 0.1-0.4 times the speed of light. This is, relatively speaking, a low speed, and the system may be treated as a perturbation, or correction, to the Newtonian description. In Newton’s theory, the black holes are just orbiting each other in a circular or elliptical orbit and there is no energy lost by way of gravitational waves which causes them to spiral towards each other (fall inwards).
In other words, the black hole pair can be described by an equation of motion based on Newtonian dynamics with appropriate correction terms which come in at higher orders. Using this approach, when one calculates the so-called post-Newtonian coefficients, they are found to match with what has been inferred from the experimentally detected signal.
Lastly, according to the General Theory of Relativity, gravitational waves must be “dispersionless” that is, the field particle associated with gravity, the graviton, must have a zero mass. This means different wavelength components of the wave would travel at the same speed. This was also verified by the form of the wave. ‘The famous “chirp” that was heard attests the dispersionless character of the component waves. Dispersion will introduce a characteristic change in the shape of the observed signal. If they had had a strong dispersion, what would have been heard is an “inverted chirp”’, says Dr. P. Ajith of the International Centre for Theoretical Sciences, Bengaluru.
