Space Phenomenon

1.3 Black Holes and Einstein Rosen Bridges

In 1963, the New Zealand mathematician Roy Kerr found that if a black hole is rotating a singularity still forms, but in the form of a ring, not a point. It was believed that in principle a particle may be able to fall towards the singularity but if at some point it moved through the hole instead of the ring the particle may not be lost forever. When this was published black holes were not believed to exist and therefore the Kerr solution only really developed in the 1970s, after astronomers discovered what seem to be real black holes.

Hawking 1988 and John Gribbin Homepage

Unfortunately, more modern work published in late August 1998 by Piran and Shahar Hod has seemingly ended this idea. They used complex computer simulations to study how an electrically charged black hole might form and how the singularity would behave. It was the first time that a single computer program has simulated these two processes at once.

They showed that a process known as "mass inflation" violated the Kerr hypothesis. When a particle moves towards the black hole, the apparent mass of the hole increases to infinity as observed by the object. (Physical Review Letters, vol 81, p 1554). "This singularity goes through the entire system," says Piran. "It doesn't leave any hole through which matter may pass."

New Scientist, 5 September 1998

The use of black holes as objects that may aid interstellar travel was to be included in a novel called Contact. While writing the novel in 1985 Sagan turned to for advice to Kip Thorne, at CalTech. Sagan wanted a method of moving a character faster than light though not in a manner violating Relativity. Thorne set two of his PhD students, Michael Morris and Ulvi Yurtsever, the task of working out some details of the physical behaviour of "wormholes". This story often appears to attribute the discovery of wormholes to Thorne or Sagan. In fact, they were investigated almost as soon as Einstein published General Relativity, far before black holes were established to exist. 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.


Indeed, Einstein himself, working at Princeton with Nathan Rosen in the 1930s, had discovered that the equations actually represent a black hole as a bridge between two regions of flat space-time a phenomenon known as an "Einstein-Rosen bridge". A black hole always has two "ends", a property ignored by everyone except a few mathematicians until the mid-1980s.

Morris and Yurtsever found that this widely held belief was wrong. By starting out from the mathematical end of the problem, they constructed a space-time geometry that matched Sagan's requirement of a wormhole that could be physically traversed by human beings. Then they investigated the physics, to see if there was any way in which the known laws of physics could conspire to produce the required geometry. To their own surprise, and the delight of Sagan, they found that there is.

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.

Contrary to the work of Piran and Shahar Hod, some believe that adding electric charge to a black hole provides it with a second field of force, in addition to gravity that may act as an antigravity force. This is because charges with the same sign repel one another. Rotation does much the same and in either case, there is a force that opposes the inward tug of gravity. Even though an electric field, or rotation, may hold an Einstein Rosen Bridge open turning around to go back the way you came would require travelling faster than light. The problem arises due to the fact that an accelerating object, according to General Relativity, generates ripples in the fabric of space-time known as gravitational waves. Gravitational radiation itself, travelling into the black hole at the speed of light, could be amplified to infinite energy as it approaches the singularity inside the black hole, warping spacetime around itself and shutting the door on the particle moving into the singularity

The way Morris, Yurtsever and Thorne set about the problem posed by Sagan was the opposite of the way everyone before them had thought about black holes. They worked backwards and started out by constructing the mathematical description of a geometry that described a traversable wormhole. They then used the equations of the general theory of relativity to work out what kinds of matter and energy would be associated with such a space-time. The difference here being that they did not look for an object and try to describe the effects it may have. More over they looked at the effects and tried to extrapolate to an object that might create them.

Yurtsever and Thorne found that gravity, tends to create singularities and to pinch off the throat of an Einstein Rosen Bridge. The equations said that in order for an artificial wormhole to be held open, its throat must be threaded by some form of matter, or some form of field, that exerts negative pressure, and has antigravity associated with it.

John Gribbin Homepage

Richard F. Holman a professor of physics at Carnegie Mellon University explained this in an interview with Scientific American. He stated that though wormhole geometries are inherently unstable. He believed that to stabilise them against closure would require material having a negative energy density, at least in some reference frame. Though no classical matter can do this he holds the belief that quantum fluctuations in various fields might be able to.

Scientific American Website

William A. Hiscock of Montana State University, Bozeman, explained that extensive work by scientists such as L.H. Ford and T.A. Roman, Brett E. Taylor, William A. Hiscock and Paul R. Anderson and others on the behaviour of quantized fields demonstrated that quantum field effects could hold open a macroscopic wormhole.

Scientific American Website

Alternatively, David Hochberg, A.D. Popov and Sergey V. Sushkov have found a wormhole solution using approximate expressions for a quantized scalar field. Their work included a number of assumptions concerning the (unknown) parameters of quantum gravity in their work.

Types of Einstein Rosen Bridges

There are two main types of wormhole of interest to physicists: Lorentzian wormholes (general relativity) and Euclidean wormholes (particle physics).

Lorentzian wormholes are essentially short cuts through space and time but as discussed above they close instantaneously unless some form of negative energy can hold them open. It is possible to produce small amounts of negative energy in the laboratory by a principle known as the Casimir effect. Unfortunately, this is very far removed from the kinds of energy required to keep the "throat of a wormhole open.

Atkins 1983 and Hawking 1988

A by product of Lorentzian wormholes would be that objects passing through them would not only be moved spatially but also temporally. This effect of Einstein Rosen Bridges led Stephen Hawking to promulgate his Chronology Protection Conjecture. According to this conjecture, quantum effects will conspire to effectively prevent time travel even when it looks like classical physics might allow time travel to occur. Euclidean wormholes are even stranger given that they live in "imaginary time" and are intrinsically virtual quantum mechanical processes. These Euclidean wormholes are of interest mainly to the particle physicists (quantum field theorists).

Scientific American Homepage

Stephen Hawking conjectured that while wormholes might be created, they cannot be used for time travel; even with exotic matter stabilising the wormhole against its own instabilities. Hawking argued, inserting a particle into an Einstein Rosen Bridge will destabilise it quickly enough to prevent its use.

Israeli researcher. Amos Ori, of the Technion-Israel Institute of Technology, in Haifa, has found a flaw in the above argument. Without violating General Relativity Ori has found that mathematical solutions exist of space-times which loop back upon themselves in time. However, Ori’s theory states that no singularity appears early enough to interfere with the time travel, and the weak energy condition is satisfied.

(Physical Review Letters, vol 71 p 2517).
New Scientist
Cambridge Relativity and Cosmology public home pages

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