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Waves

A classical way of picturing the manner in which heavy bodies curve space is to imagine a rubber sheet. When a small metal ball is made to roll on it it will go in a straight line at constant speed (neglecting friction). Now imagine that a heavy metal ball is placed in the middle of the sheet; because of its weight the sheet will be depressed in the middle (Fig 7.13). When a small ball is set rolling it will no longer follow a straight line, its path will be curved and, in fact, it will tend to circle the depression made by the heavy ball. The small ball can even be made to orbit the heavy one (it will eventually spiral in and hit the heavy ball, but that is due to friction, if the sheet is well oiled it takes a long time for it to happen). This toy then realizes what was said above: a heavy mass distorts space (just as the heavy ball distorts the rubber sheet). Any body moving through space experiences this distortion and reacts accordingly.

Now imagine what happens if we drop a ball in the middle of the sheet. It will send out ripples which spread out and gradually decrease in strength. Could something similar happen in real life? The answer is yes! When there is a rapid change in a system of heavy bodies a large amount of gravitational waves are produced. These waves are ripples in space which spread out form their source at the speed of light carrying energy away with them.

A computer simulation of a gravitational wave is given in Fig. 7.19. The big troughs denote regions where the wave is very intense, the black dot at the center denotes a black hole, the ring around the hole represents the black hole's horizon.


 
Figure 7.19: A computer simulation of a gravitational wave generated by a collision of two black holes, which have now merged and are represented by the heavy black dot in the middle. 
\begin{figure}
\centerline{ \vbox to 3.3 truein{\epsfysize=4 truein\epsfbox[0 0 612 792]{7.gtr/grav_wave.ps}} }\end{figure}

Can we see gravitational waves? Not yet directly, but we have very strong indirect evidence of their effects. Several systems which according to the General Theory of Relativity ought to lose energy by giving off gravitational waves have been observed. The observations show that these systems lose energy, and the rate at which this happens coincides precisely with the predictions from the theory.

Observing gravitational waves directly requires very precise experiments. The reason is that, as one gets farther and farther away from the source these waves decrease in strength very rapidly. Still, if a relatively strong gravitational wave were to go by, say, a metal rod, its shape would be deformed by being stretched and lengthened periodically for a certain time. By accurately measuring the length of rods we can hope to detect these changes. The technical problems, however, are enormous: the expected variation is of a fraction of the size of an atom! Nonetheless experiments are under way.

Gravitational waves are generated appreciably only in the most violent of cosmic events. During the last stages in the life of a star heavier than 3 solar masses, most of the stellar material collapses violently and inexorably to form a black hole (n the rubber sheet picture this corresponds to dropping a very small and very heavy object on the sheet). The corresponding deformation of space travels forth from this site site as a gravitational wave. High intensity gravitational waves are also produced during the collision of two black holes or any sufficiently massive compact objects


next up previous contents
Next: Summary. Up: The General Theory of Previous: Curvature
Jose Wudka
9/24/1998