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The Einstein connection

The Einstein connection



It's one of the intriguing curiosities of the history of science that spacetime wormholes were actually investigated by mathematical relativists in great detail long before anybody took the notion of black holes seriously. As early as 1916, less than a year after Einstein had formulated his equations of the general theory, the Austrian Ludwig Flamm had realised that Schwarzschild's solution to Einstein's equations actually describes a wormhole connecting two regions of flat spacetime -- two universes, or two parts of the same universe. Speculation about the nature of wormholes continued intermittently for decades. What the pioneering relativists did establish, very early on, was that Schwarzschild wormholes provide no means of communicating from one universe to the other.

The problem is that in order to traverse an Einstein-Rosen bridge from one universe to the other, a traveller would have to move faster than light at some stage of the journey. And there is another problem with this kind of wormhole -- it is unstable. If you imagine the "dent" in spacetime made by a large mass such as the Sun, squeezed into a volume only slightly bigger than its corresponding Schwarzschild sphere, you would get an "embedding diagram". The surprise about the Schwarzschild geometry is that when you shrink the mass down to within its Schwarzschild radius, you don't just get a bottomless pit; instead, the bottom of the embedding diagram opens out to make the connection with another region of flat spacetime . But this beautiful, open throat, offering the tantalising prospect of travel between universes, exists for only a tiny fraction of a second before it snaps shut.

The wormhole itself does not even exist for long enough for light to cross from one universe to the other. In effect, gravity slams shut the door between universes. This is especially disappointing, because if you ignore the rapid evolution of the wormhole and only look at the geometry corresponding to the instant when the throat is wide open, it seems as if such wormholes might even connect, not separate universes but separate regions of our own Universe. Space may be flat near each mouth of the wormhole, but bent around in a gentle curve, far away from the wormhole, so that the connection really is a shortcut from one part of the Universe to another . If you imagine unfolding this geometry to make the entire Universe flat except in the vicinity of the wormhole mouths, you get something , in which a curved wormhole connects two separate regions of a completely flat Universe -- and don't be fooled by the fact that in this drawing the distance from one mouth to the other through the wormhole itself seems to be longer than the distance from one mouth to the other through ordinary space; in the proper four-dimensional treatment, even such a curved wormhole can still provide a shortcut from A to B.

Or at least, it could if the wormhole stayed open for long enough, and if passage through the wormhole didn't involve travelling at speeds faster than that of light. But this is not the end of the story of hyperspace connections. A simple Schwarzschild black hole has no overall electric charge, and it does not rotate. Intriguingly, adding either electric charge or rotation to a black hole transforms the nature of the singularity, thereby opening the gateway to other universes, and makes the journey possible while travelling at speeds less than that of light.

Adding electric charge to a black hole provides it with a second field of force, in addition to gravity. Because charges with the same sign repel one another, this electric field acts in the opposite sense to gravity, trying to blow the black hole apart, not pulling it more tightly together. Rotation does much the same. There is a force, in either case, that opposes the inward tug of gravity.

Although gravity still tries to slam shut the door opening to other universes, the electric field, or rotation, holds the door open for travellers to get through. But there is still a sense in which this is a one way door; you could not get back to the universe you started from - - you would inevitably emerge into another region of spacetime, usually interpreted as another universe. What goes in one end (the black hole) comes out of the other end (sometimes dubbed a white hole). Turning around to go back the way you came would require travelling faster than light.

Until Sagan made his innocent enquiry about wormholes to Thorne, this was the nearest the mathematicians had come to describing a plausible traversable, macroscopic wormhole.

New speculations, encouraged by Sagan's wishful thinking and developed by the CalTech researchers and others, suggest that it might indeed be possible to construct traversable wormholes artificially, just as Sf writers have been telling us for decades, given a suitably advanced technological civilization.




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