Sonic Black Hole A chapter excerpted from The Jazz of Physics, published by Basic Books, May 2016, with permission of the author. PHOTOGRAPH BY LENDEL MARSHALL Lurking in every active galaxy in our cosmic web is the densest and most elusive object known to physics, the black hole. m 14 Stephon Alexander By STEPHON ALEXANDER It was one of the very first exactly solvable systems in Einstein’s theory of warped space and time — general relativity and at first was thought to be a purely theoretical construct. Recently, after 100 years, technology was developed by the Laser Interferometer Gravitational Wave Observatory (ligo) that for the first time “heard” the swirling waves of gravitational ripples emanating from two binary-black holes that merged elevating them from mere mathematical constructs to a part of our reality. But black holes are mysterious in that they are cloaked by a horizon, similar to the horizon we see on the far stretches of the ocean. By exploring the role of horizons surprisingly to sound, in the case of black holes, we will gain a deeper intuition in our search to link music with cosmic structure. The difficulties in dealing with Einstein’s ten coupled equations of the gravitational field of space and time, versus Newton’s one equation, are enormous. To get a sense of the complexity we have in front of us, imagine a simplified analogy of the bending of space as a series of masses on springs linked together and in motion. Newton’s differential equation can be applied to the movement of one independent mass. But because the masses are linked, the motion of one will influence the motion of those it is attached to and hence affect their equations of motion. A set of interdependent equations is needed to determine the overall motion of all the springs and hence the total system of springs. To solve one equation, you are required to solve them all. A similar situation arose in the Ising model of magnetism discussed in an earlier chapter in the book, where the spins of neighboring atoms influenced each other and hence the overall interaction energy of the system. The difficulties are compounded when we recall that Einstein’s equations couple not just mass with mass but mass with space and time.