# NYU Black Renaissance Noire NYU Black Renaissance Noire V. 16.1 - Page 19

k A sonic horizon can be understood with a waterfall. A fish emits a sound, denoted by the circles, but the speed of the sound is much slower than the speed of the waterfall, so it never gets to the upstream fish. l The white and black regions represent sound waves “played” by a black hole in the Perseus cluster.1 == K r — This equation relates the speed of sound, c, to the stiffness of the medium, K, and the density of the medium, . The equation is telling us that the speed of sound increases with the stiffness of the material but decreases with increasing density. Sound will travel slower in a denser gas, such as oxygen, rather than helium, yet will travel faster through stiffer materials, like solids. Though solids are more dense than gases, and so one might think sound would travel slower in them, solids are far stiffer than gases, speeding up sound travel. So to understand the black hole horizon, Bill imagined a fish going downstream while a fishy friend remains upstream. At some point, the downstream fish takes a plunge down a waterfall. The speed of the water in the waterfall far exceeds the speed of the water upstream because gravity has given it a boost. Rushing downward, the fish screams, hoping that his friend will hear, “Hey, I’m falling!” But sound is a wave, and as the above equation illustrates, it moves at a fixed velocity in a uniform medium. If the speed of the waterfall is much faster than the speed of the fish’s sound wave moving upstream, then the sound wave will never get to the other side of the waterfall for his friend to hear him. An uphill battle, lost. To the fish falling down the waterfall, the sound can be heard, but to his friend on the other side, there is silence. The edge of the waterfall is a sonic horizon. The black hole solution in general relativity had a predictive power that few physicists anticipated — the surprising reality of the event horizon. According to the black hole solution, if the fish fell through the event horizon, no matter how hard the fish tried to communicate with his friend outside the black hole, his message would never escape to the other side of the horizon. Even more sad, once the fish falls through the horizon of the black hole, he would have no hope of coming back out. Not even a salmon could thrash his way out of this. Not only do black hole horizons have a sonic quality, but it was recently discovered that some black holes play a drone-like song. The figure above shows the sound wave generated by a black hole at the center of a galaxy in the Perseus cluster. The note of the black hole’s sound was identified as a B-flat fifty octaves below middle C on a piano. The existence of horizons is a general feature of Einstein’s theory and has serious consequences for the discussion of the space-time structure of our universe. This is true of both black holes and the cosmic horizon. The cosmic horizon, however, is a bit different from an event horizon. Unlike a black hole, it is a two-way avenue, where light and matter cross both ways, depending on the interplay between the expansion of the universe and the passage of time. Though black hole horizons are distinct because of the immense gravitational forces involved, they have helped us understand how a horizon can act as a boundary. It is the existence of such a boundary, the cosmic horizon, at the time that the cmb light was released, when the first stable atoms were formed, that created resonances in the cmb anisotropies. Just like bridges on a guitar provide the boundaries necessary for a string to resonate and create notes, the cosmic horizon allows for discrete notes in the matter perturbations of the universe. What causes these vibrations fixed by the cosmic horizon fret board? Today physicists are still mystified by black holes. We see them at the center of our own galaxy; they seem to play a central role in birthing new stars, but we still don’t know what lurks beyond their horizons. Could it be the harmony of a new universe? n BLACK RENAISSANCE NOIRE c2 To the upstream fish, his friend simply disappeared — out of sight, out of earshot, and, for fish, out of mind. Of course, if he called out to his lost friend, the so und would travel nicely downstream and over the edge of the waterfall, aided by the flow of the water. This is how light behaves around the event horizon of a black hole. Light can enter the black hole easily, but exiting is another failed story. 17 We can calculate the speed of sound in water using the basics of wave mechanics. Consider the following equation: