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: