-Z- (z@gundam.com)
Fri, 17 Nov 2000 18:10:44 -0800


> -----Original Message-----
> From: owner-gundam@1u.aeug.org [mailto:owner-gundam@1u.aeug.org]On
> Behalf Of Lim Jyue
> Sent: Thursday, November 16, 2000 20:21
> To: gundam@aeug.org
> Subject: RE: [gundam] What about Minovski Drives? (Re: Long!] Minovsky
> Applications Theories)
>
> >There is no limit in principle to how much or how little mass a black hole
can
> >have. Any amount of mass at all can in principle be made to form a black
hole
> >if you compress it to a high enough density.
>
> In principle -- if you accelerate a particle towards light speed
> (and hence gaining mass), and assuming the size of the particle do not
> change, is it possible to get a black hole from there?

This is supposedly something that actually happened during the Big Bang -- the
enormous pressures compressed particles of matter in "quantum" black holes.
Larry Niven used to write about Belters finding quantum black holes in Asteroids
and using them for power sources, until Stephen Hawking showed that black holes
aren't totally black -- they emit radiation and "evaporate" over time -- and
proved that any quantum black holes that might have existed have long since
self-destructed. Later Niven stories using quantum black holes had them formed
either artificially, using gravity-based technologies far beyond anything
available in the Gundam world, or by natural events much more recent than the
Big Bang, involving supernova or some such.

And it appears that I misspoke whent I said that there was no limit to how
little mass a black hole can have. The smallest possible black hole is around
10^-35 meters across, the so-called Planck Length -- anything smaller just gets
wiped out by the quantum fluctuations in space-time around it. But even such a
tiny black hole would weigh around 10 micrograms -- about the same as a speck of
dust.

To create objects with so much mass demands energies of 1,019
giga-electronvolts, so the most powerful existing collider is ten million
billion times too feeble to make a black hole. Scaling up today's technology,
we would need an accelerator as big as the entire galaxy to do it.

To get a black hole worth the effort, you'd also need to start with at least a
planetary mass. Even a black hole with the mass of Mount Everest would have a
radius of only about 10 to 15 meters, roughly the size of an atomic nucleus.
Current thinking is that it would be hard for such a black hole to swallow
anything at all -- even consuming a proton or neutron would be difficult

> Is this referred to as the event horizon? I understand that the
> Schwarzschild radius is the radius where light particles would orbit at,
> unable to ever escape the black hole without additional help.

No, the Schwarzchild radius is the radius of the black hole proper. The event
horizon is the boundary of space-time around the black hole that separates it
from the rest of spacetime.

The idea of a mass concentration so dense that even light would be trapped goes
all the way back to Laplace in the 18th Century. Almost immediately after
Einstein developed general relativity, the German astronomer Karl Schwarzschild
(1873-1916) discovered a mathematical solution to the equations of the theory
that described such an object. It was only much later, with the work of such
people as Oppenheimer, Volkoff, and Snyder in the 1930s, that people thought
seriously about the possibility that such objects might actually exist in the
Universe. These researchers showed that when a sufficiently massive star runs
out of fuel, it is unable to support itself against its own gravitational pull,
and it should collapse into a black hole.

In general relativity, gravity is a manifestation of the curvature of spacetime.
Massive objects distort space and time, so that the usual rules of geometry
don't apply anymore. Near a black hole, this distortion of space is extremely
severe and causes black holes to have some very strange properties, one of which
is the event horizon. This is a spherical surface that marks the boundary of
the black hole. You can pass in through the horizon, but you can't get back
out. In fact, once you've crossed the horizon, you're doomed to move inexorably
closer and closer to the "singularity" at the center of the black hole.

You can think of the horizon as the place where the escape velocity equals the
velocity of light. Outside of the horizon, the escape velocity is less than the
speed of light, so if you fire your rockets hard enough, you can give yourself
enough energy to get away. But if you find yourself inside the horizon, you
can't escape. It's the Point of No Return projected into a sphere.

The horizon has some very strange geometrical properties. To an observer who is
sitting still somewhere far away from the black hole, the horizon seems to be a
nice, static, unmoving spherical surface. ("Frozen" in time, remember?) But
once you get close to the horizon, you realize that it has a very large
velocity. In fact, it's moving outward at the speed of light! That's why it's
easy to cross the horizon in the inward direction, but impossible to get back
out. Since the horizon is moving out at the speed of light, in order to escape
back across it, you would have to travel faster than light. You can't go faster
than light, and so you can't escape from the black hole.

The horizon is, in a certain sense, sitting still, but, in another sense, it's
flying out at the speed of light. It's a bit like Alice in "Through the
Looking-Glass": she has to run as fast as she can just to stay in one place.
But that same sort of balancing act is aprt of the orbital dynamic we see
everyday in a geosynchronous satellite. It one sense, it's stationary, holding
a fixed position directly above the point on Earth whose rotational speed it
matches. In the other sense, it's a ballistic missile falling around the planet
at 20 times the speed of sound, making one complete orbit every 23 hours, 56
minutes and 5 seconds.

Once you're inside of the horizon, spacetime is distorted so much that the
coordinates describing radial distance and time switch roles. That is, r, the
coordinate that describes how far away you are from the center, is a timelike
coordinate, and t is a spacelike one. One consequence of this is that you can't
stop yourself from moving to smaller and smaller values of r, just as under
ordinary circumstances you can't avoid moving towards the future, towards larger
and larger values of t. Eventually, you're bound to hit the singularity at r =
0. No matter which direction you try to go, you can't avoid your future.
Trying to avoid the center of a black hole once you've crossed the horizon is
just like trying to avoid next Thursday.

-Z-

-
Gundam Mailing List Archives are available at http://gundam.aeug.org/



This archive was generated by hypermail 2.0b3 on Sat Nov 18 2000 - 10:55:17 JST