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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.

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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.