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On Fri, 9 Jul 1999, Karl wrote:
> Due to Newtons law, the gravitation becomes
> bigger when the distance is small. What's the
> gravitation in the centre of the earth, or in
> a singularity in a black hole?
The gravitation in the center of the Earth is close to zero. You are
correct that the force of gravity depends upon the distance from the
center of an object, but it also depends upon the amount of mass between
you and the center of the object. If we were to travel to the middle of
the Earth, as we went, we would leave more and more of the Earth's mass
outside of our radius. The gravitational pull due to this mass cancels
out (it's a tricky calculus problem, but it does work out), and so only
the mass interior to our location would contribute to the gravitational
pull of the Earth. So, at the center of the Earth, gravity is zero, but
the pressure of the rock from above would be immense!
Within a black hole, it is uncertain what happens to the gravitational
field. If a singularity exists, then the force of gravity would be
infinite. But, in truth, nobody is certain. I believe that two of the
best physical minds, Stephen Hawking and Kip Thorne, have running bets as
to the outcome to this problem.
> How to you explain the Schwarzschild and the
> Kerr-Newman metric?
Black holes have three measurable properties according to general
relativity: mass, spin, and charge. A Schwarzschild metric is just a
simplification of Einstein's theories assuming that the black hole is not
spinning and has a neutral charge. It is the simplest case to work out.
A Kerr metric introduces rotation, and is more complex to solve. And the
Kerr-Newman solution includes both charge and rotation in addition to
mass, and is therefore the most general (and most complicated) solution to
Einstein's equations. Most astronomers don't bother with the Kerr-Newman
solution, since all known large objects in the Universe are have no
significant charge to them.
> Do you believe there are graviation waves?
Gravitational waves are predicted by Einstein's general relativity
equations, and are very similar to electromagnetic waves (light).
Gravitational waves carry gravitational energy away from a system.
However, their amplitude is extremely small once you get very far from an=
object. Two scientists named
Hulse and Taylor discovered two pulsars orbiting around each other. (A
pulsar is a spinning neutron star, created by the collapse of the core of
a dying star.) Pulsars are better clocks than the best atomic clocks on
Earth, and so Huilse and Taylor were able to measure the orbit of the two
stars with extreme (even absurd) accuracy. They discovered that the two
pulsars are slowly moving closer together, which means that gravitational
energy must be leaving the system. The amount of energy seen to be
leaving the binary pulsar and the amount of energy predicted to be
produced by gravitational waves matched, and so it is virtually certain
the gravitational waves exist. For this Hulse and Taylor won the Nobel
prize. Currently, a gravitational wave detector called "LIGO" is being
built in the U.S. which should be able to see the largest gravitational
waves, so soon we will know without a doubt that gravitational waves
exist.
> What happens to information that falls into a
> black hole?
As I mentioned above, information on a particle's mass, charge and angular
momentum (rotation) are added to the black hole and can be observed from
the outside. Stephen Hawking also discovered that information on the=20
amount of entropy (the amount of "order" to the universe) is also
observable from the outside. Other information, such as the types of
particles that fall in, currently seems to be lost forever. Exactly how
(or even if) this information is lost to our universe remains a subject of
debate.
Thanks for writing!
Sincerely,
Kurtis Williams
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