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SEPTEMBER/OCTOBER 2019
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DISCOVER 71
Unlike the immobile, perfectly rounded
Schwarzschild black holes, rotating black holes have
bulges at their equators (just as Earth and the sun do).
Because they lack the symmetry of a sphere, model-
ing them becomes a much more computationally
demanding endeavor.
“The biggest thing we did to make the task doable
was to spend much more time thinking about solving
the problem than actually solving it,” says Chesler.
That meant determining the optimal choice of coor-
dinates and coordinate system they’d use to describe
their simulated black hole — literally, how they’d mea-
sure, model and navigate the space around it. Think
back to high school math: You might use Cartesian
coordinates when it’s convenient to represent points
by their latitude and longitude (or x and y positions).
But sometimes it’s easier to identify points by their
polar coordinates — their distance and direction from
a common origin.
Picking the proper coordinates and coordinate
system is analogous to choosing the best directions
and map before setting off on a road trip and knowing
which landmarks to keep an eye
out for along the way. A poor
choice of coordinates could
make the physics problem
unsolvable, just as poor direc-
tions may not get you to your
destination. A good choice of
coordinates, on the other hand,
can make the computational
chore much more manageable.
After laying the groundwork, the researchers were
ready to begin the actual simulation. “We start with
the equations of general relativity,” Chesler explains,
“specify some initial conditions, and then see how
things evolve as we move forward in time.” The simu-
lation worked out the geometry of space-time inside
a Kerr black hole — about the same as determining
the gravitational field, according to Einstein’s theory.
Once the geometry had been established, the simula-
tion could describe the trajectory of incoming light
rays — essentially revealing the black hole’s interior
structure. The whole computation was performed
CARTESIAN POLAR
Different coordinate
systems are best for
different problems.
Cartesian coordinates,
with their straight
lines, work differently
than polar coordinates,
which focus on
distance and direction
from a central point.
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