| Topic: |
Science > Physics |
| User: |
"Tom Roberts" |
| Date: |
04 Apr 2004 10:33:40 PM |
| Object: |
Re: Negative energy and a white/worm hole |
Ed Keane III wrote:
The Schwarzschild metric admits negative square
root as well as positive square root solutions for the
geometry.
Hmmm. I see no square-root in the Schwarzschild metric. And when you
solve the geodesic equation, square-roots do not come in, either. So I
don't know what you mean, here.
This allows a white hole or anti-black hole.
The Schwarzschild manifold itself has one, plus its well-known black
hole. This is not at all obvious if you just look at the Schwarzschild
coordinates. But sometime in the 1960s or so Kruskal introduced new
coordinates (that bear his name) and used them to show that the
Schwarzschild manifold has "two universes", and two singularities, one a
black hole and one a white hole. No non-spacelike object can get from
one "universe" to the other, and no non-spacelike object can approach
the white hole. Schwarzschild coordinates for r>2M cover only one of the
"universes", and for 0<r<2M only cover half the region inside the
horizon -- there are two more regions that are not causally related to
those.
I am wondering about something different. Could there
be an area of space containing a concentration of
negative energy and what would its properties be?
Negative energy density has never been observed experimentally (except
one might interpret the Casimir effect to be "negative energy density"
in a very small region; this is not definitive, however).
Today, GR includes a postulate that negative energy does not exist. This
does not prevent people from exploring what negative energy density
would mean, and numerous "warp metrics" are known, in which timelike
objects can be transported at speeds much larger than c relative to
certain global coordinates -- the LOCAL speed limit is obeyed, but these
metrics have peculiar global properties....
Negative energy density is not directly related to white holes. A white
hole is just a different kind of singularity than is a black hole.
The absence of negative energy density is a requirement of the various
singularity theorems.
An area containing negative energy would not spout
energy or gravitationally repel. [...]
What would happen depends in detail on the configuration of whatever it
is that generates the negative energy density. Just like for normal
matter, it is the full energy-momentum tensor that contributes to the
curvature of spacetime (and therefore to its geometry), not just the
energy density. The things you claim are reasonably plausible _IF_
negative energy density existed....
Tom Roberts tjroberts@lucent.com
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