Black hole studies to verify Einstein's
theory
by Randall Graham, Science Writer
Recent government approval to fund
construction of two Laser Interferometric
Gravi-tational Wave Observatories
(LIGOs) has increased the urgency
with which NCSA research scientist
Ed Seidel and his NCSA colleagues
(Peter Anninos, David Bernstein,
Steve Brandt, Karen Camarda, Larry
Smarr, and John Towns) are seeking
to define the gravitational wave
signatures of black holes via theory.
If LIGO researchers are to tell true
gravitational waves from false readings,
the signatures are important.
In about five years, the LIGOs should
be operational. And they will attempt
to experimentally measure-- for the
first time--the gravitational waves
predicted by Einstein's theory of
general relativity. Such a breakthrough
would help prove that Einstein's
theory of gravity is correct.
The LIGOs will be two of the most
sensitive measuring instruments ever
built--able to detect variations
in the Earth's gravitational field
on the order of one one-millionth
of a nuclear radius over 1 meter.
This would be like measuring a variation
of one angstrom in the distance from
the Earth to the Sun.
Einstein's gravity
Einstein's theory of general relativity
defines gravity as variations in
the curvature of spacetime and predicts
that cataclysmic astrophysical events,
such as exploding supernovas or colliding
black holes, send gravitational waves
rippling through the curved geometry
of the universe. Although they are
very weak, the waves should create
a detectable gravitational disturbance
as they pass Earth. Each type of
phenomenon should generate a unique
wave signature that scientists can
decipher to trace the source.
"Gravitational waves should also
tell us a lot about astrophysics,"
says Seidel. "The waves respond to
the bulk motion of a large amount
of mass. The coherent bulk motion
of two stars coalescing or of a nonspher-ical
supernova blowing up will yield a
wave form that is the only indicator
of what the sum of that mass is doing.
Currently nothing provides us with
information about this 'big picture.'
For example, electromagnetic radiation
comes from a small local unit like
a molecule, but the gravitational
wave comes from the global mass.
A whole new field of science could
spring up around the interpretation
of gravitational waves."
Developing a gravitational wave catalog
One of Seidel's goals is to use super-computers
to provide part of a wave signature
catalog for LIGO researchers to help
them recognize the sources of detected
waves. At the same time, the theoretical
framework developed in making the
catalog should provide researchers
with a means of tracing unknown
LIGO signatures in the future.
"I expect that once LIGO is operational
there will be some wave forms detected
that we can't explain," says Seidel.
"Once we're able to solve Einstein's
equations, we should be able to go
back and figure out, from a theoretical
point of view, what the source of
that wave is."
Understanding black hole resonance
Recently Seidel and his colleagues
created an animation of one- and
two- black hole systems using the
Silicon Graphics VGX system. The
video shows the evolution of apparent
black hole horizons in settings where
the holes are distorted initially
and then allowed to snap back to
their stable, equilibrium state.
(The apparent horizon is defined
as a mathematical boundary surrounding
a black hole at which outgoing light
rays are trapped and are no longer
expanding away from the hole.)
The animation illustrates that black
holes seek to maintain a spherical
apparent horizon and that two colliding
black holes will quickly coalesce
into one stable black hole. It also
shows that both one- and two-hole
systems will oscillate with a mass-dependent
resonant frequency.
"Most systems have a normal mode
frequency," says Seidel, "just like
a bell. If you hit a bell, it rings
with a certain frequency. Different
sized bells have different frequencies.
Black holes also have special frequencies--only
the wave being propagated is a gravitational
wave."
Seidel's group chose the SGI 360VGX
system to produce the video because
of its power and built-in animation
capabilities. "SGI's VGX was the
best machine for making our animation
because its built-in graphics hardware
and software make it very fast,"
says Seidel.
The 360VGX contains six RISC-based
MIPS architecture CPUs. It employs
85 proprietary graphics processors
contained in four pipelined graphics
subsystems. Visual data from the
RISC host is processed by these subsystems
before being displayed on the screen,
and parallelism is exploited extensively
throughout the system.
Searching for a missing part of the
two-hole wave form
For some time scientists have understood
the wave form for two black hole
systems during two stages: when the
holes are far apart and after they
have collided. NCSA Director Smarr's
Ph.D. thesis in 1975 was dedicated
to building the computing and theoretical
understanding of what happens as
the two holes approach and influence
one another.
Says Seidel, "For the two-black hole
system, we can calculate the beginning
wave form using an approximation
of Einstein's theory or even Newton's
laws. And we can calculate the ending
wave form after the two have collided
using perturbation theory. But there
is no easy way to calculate what
happens as they approach one another
and interact. Here we need a supercomputer
because we have to solve the full
Einstein equations with no approximations.
Our group has made a great deal of
progress on the two-black hole collision
when it occurs head-on, because then
the problem is axisym-metric."
A solution to the full dynamic 3-space
Einstein equations is still out of
reach. But a recent visitor, graduate
research associate Joan Masso from
Spain's Universitat de les Illes
Balears, developed a promising new
approach to the equations that may
help realize this goal.
A new, easier way to write Einstein's
full equations
Masso and his advisor, Carles Bona,
came up with a new way of writing
the general Einstein equations in
a flux conservative form. It's a
form that allows one to use techniques
for solving hydrodynamic equations
and apply them to Einstein's equations
for the first time.
"Masso's approach lets us take well-developed
hydrodynamic numerical techniques
and apply them to the Einstein equations,"
says Seidel. "Unfortunately you do
give up something with this method,
and we're trying to figure out a
way to minimize it. The time coordinate
necessary for this method to work
allows you to get very close to the
black hole. And that's bad numerically,
because you want to stay away from
anything where the numbers are becoming
infinite when using a computer. Their
system of equations depends crucially
on this time coordinate. So we want
to figure out a way to avoid the
singularity and still use their time
slicing division. We are currently
working with Masso and also with
Wai-Mo Suen at Washington University
in St. Louis on a new approach to
avoiding singularities. If we can
do that, then their form of the equations
could definitely improve the numerical
solution to the Einstein equations."
Next year Masso may return to NCSA
as a postdoctoral visitor and continue
work on his techniques.
"One thing we would like to do,"
says Seidel, "is generate a solver
for the Einstein equations and some
kind of interface through Mathematica
or some other symbolic manipulator.
That way, someone working on exact
solutions of the Einstein equations
using purely analytic techniques
could look at our solution and explore
the analytic behavior of it."
Solving Einstein's equations: A Grand
Challenge
"This whole incredible field of black
hole physics has come out of the
one solution to Einstein's equations,
the Schwarzschild solution. It was
developed the year after Einstein's
theory was published, and it's a
simple spherical solution," Seidel
continues.
"Just think what would happen once
we develop the technology to solve
the general Einstein equations. The
knowledge about these equations could
just explode--especially if we made
it possible for people used to pursuing
analytic solutions to take their
symbolic manipulators and look at
one of our solutions. And when I
say 'our' solutions, I'm referring
to solutions generated by our group
or by those of our collaborators
and colleagues at other institutions--such
as the University of Texas, the University
of North Carolina, Cornell University,
the University of Pittsburgh, and
Northwestern University, among others.
These research groups are planning
to work together to develop a solution
for the general Einstein equations
since this is such a difficult Grand
Challenge problem."
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