9.4 Gravitational Waves


Look deep into nature, and then you will understand everything better. Albert Einstein (1879–1955)


The detection of gravitational waves from colliding black holes opens a new window onto the universe. Can these waves be used to image the interior of our Earth?


First proposed by Henry Poincaré in 1905, gravitational waves were predicted by Einstein as part of his famous theory on general relativity in 1915. One hundred years after his prediction, in September 2015, a gravitational wave was observed simultaneously in the states of Washington and Louisiana in the USA. Physicists propose that it was created by two black holes merging into one – with a final mass estimated to 62 times the mass of the sun – in a cataclysmic event in the distant universe which took place 1.3 billion years ago. About three times the mass of the sun was converted into gravitational waves in a fraction of a second, with a peak power output about 50 times that of the whole visible universe, producing a transient wave-signal that is in the seismic frequency range, from 35 to 250 Hz.


9.4.1 Background


Einstein thought that gravitational waves were too weak to be detected. Based on his linearised equations he found in 1916 that the solution contains transversal waves with a propagation velocity equal to the speed of light. Tese waves originate from time variations in the mass quadrupole moment of the source. According to general relativity, any accelerated mass will cause a warping effect or small ripples in the fabric of space-time. Einstein did not support the theory of black holes, and therefore it is interesting that the first direct observation of a gravitational wave is interpreted as a merger of two black holes. Actually, in 1916 Schwartzschild found solutions to the field equations that were later interpreted as black holes, so the idea of black holes as a source for the strongest gravitational waves is also 100 years old. Te first proof of the existence of


gravity waves arrived in 1974, when Joseph Taylor and Russell Hulse discovered a binary pulsar – two extremely dense and heavy stars in orbit around each other. According to Einstein’s general theory of relativity, this system should radiate gravitational waves. (Pulsars are very compact stars that radiate radio waves with very regular variations, see Figure 9.26.) Tey found that the


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stars’ orbits changed over time – the stars were getting closer to each other – at precisely the rate predicted by general relativity, leaving no doubt that gravitational waves were emitted. For this work, in 1993 Hulse and Taylor received the Nobel Prize in Physics. However, direct measurements of gravitational waves were


not achieved, and in the 1980s several physicists suggested the building of a laboratory dedicated to this purpose – the Laser Interferometer Gravitational-Wave Observatory (LIGO).


9.4.2 The Gravitational Wave from Orbiting Masses


According to general relativity, two masses orbiting around each other lose energy through the emission of gravitational waves. Te nearest and simplest such system is the earth-sun, which is an orbiting system that is accelerated due to the fact that the earth is orbiting around the sun. Te power radiated by the sun (M) and the earth (m) system is given (Wikipedia) as: 32G4


P = –


(mM)4 5c5


(m+M) r5


where G is the gravitational constant, c is the speed of light and r is the earth-sun distance. Te negative sign means that energy


is leaving the system. Using this equation, it is straightforward to calculate that the power generated by the orbiting earth- sun system is only 200 watts. Compared, for instance, to the


Figure 9.46: An artist’s image of a binary black hole, which is a system consisting of two black holes in close orbit around each other. In the event that they merge, an immense amount of energy would be given off as gravitational waves, with distinctive waveforms that can be calculated using general relativity. The gravitational waves are created as the orbital distance between the two rotating masses decreases and their speeds increase. The frequency of the gravitational waves also increases until the black holes coalesce.


NASA


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