>>17
Here someone's already provided the explanation I'm too lazy to give:
http://episteme.arstechnica.com/eve/forums/a/tpc/f/770002407831/m/521006297831
To start, one needs to solve Einsteins field equations :
Gμν = 8πTμν
where T is the stress energy tensor, and G is the Einstein tensor given by:
Gμν = Rμν - 1/2gμνR
where Rμν is the Ricci curvature tensor, R the scalar curvature, and gμν, the metric that satisfies all of the equations here (there are 16 of them).
Now, Einstein originally believed that no solution would be found to these equations, but only one year later Karl Schwarzschild found just such a solution by assuming spherical symmetry. His answer describes space outside of stars and certain types of black holes (known as Schwarzschild Black Holes). The solution:
ds2 = -(1-2GM/r)dt2+(1-2GM/r)-1dr2+r2dΩ2
with dΩ2 being the normal differential portion of a sphere: dθ2+sin2θdφ2
Now... With a large amount of math, one can switch to what are known as the Kruskal Coordinates, T and X. They range from -infinity to +infinity, and can be related to the original r (distance from the singularity) and t (time) coordinates as follows:
X2 - T2 = (r/(2GM)-1)er/2GM
and
T/X = tanh(t/4GM)
With these variable in mind (X and T) we can create what is known as the Kruskal diagram:
Now, before proceeding further, let's identify what is on this figure. First, keep in mind that every point on the graph is actually a 2-sphere (S2) of radius r (our original distance from the singularity). The axis here, are simply our T and X coordinates defined above. The two lines that run from the bottom-left to the top-right and the top-left to the bottom-right represent the event horizon of the Schwartzschild black hole. You cross that there is no coming back Wink.(well maybe) Now 'normal' space, e.g. where we all exist right now is at r > 2GM (the event horizon distance) and all t, region I in the diagram. Now the singularity at the center of the black hole exists at X2-T2 = -1, so we exclude the regions where X2-T2 < -1... physics just doesn't exist there, this is the grey shaded regions at the top and bottom.
Now with an understanding of what the basics are and where we stand, we can discuss the regions:
* Region I: This is where we are, normal space. At you get further and further away from the black hole spacetime becomes asymptotically flat.
* Region II :This is the black hole itself. Once you cross into region II, no signal you emit can ever leave again to be heard in region I
* Region III: (here's where it gets cool) This is the 'time reverse' of region II. Nothing from region I can get in => this is a white hole! Here everything leaves the singularity.
* Region IV:Another asymtotically flat region akin to region I (here is where it could get interesting)
So this raises the possiblility, could spacetime be warped to the point where an observer could travel directly from region I to region IV? This would be a wormhole to some other point in spacetime!
The only place this can realistically happen is along the T=0 axis, e.g. we are traveling purely along the X=0 line. At the point where T=0, you would have the following:
At T=0 there is indeed a hole between region I and region IV. However for all T != 0, the hole shrinks and closes. It can be shown that it closes faster than any time-like observer (e.g. any object traveling at less than the speed of light) cannot possibly travel through it. As T > 0 the radius shrinks, and it shrinks in such a way that the neck pinches off to r=0 at a rate so great that no wormhole could exist for anyone not going greater than the speed of light to ever see.
This is why wormholes cannot exist.
Now, there are theories as to how a wormhole could exist, but they are merely speculation and have little to no grounding in reality. IF some form of exotic matter (something with a negative energy denisty) existed, then it is postulated that a wormhole could be created an be stable. However, no such beast is known, or (to my knowledge) realistically postulated.