Astronomers like to think they know where the stars are. They can point to them in the night sky: there's Polaris, there's Vega, there's Adhara... We've had the night sky mapped for millennia now. But how do we know the maps are right? After all, no one has been out to check that the stars really are where we think they are.

Our celestial maps are based on the assumption that photons of light almost always travel from the stars to our telescopes on Earth in a straight line. Is that a fair assumption? Maybe not. "The universe is roughly 13 billion years old: a lot of things could have happened to photon trajectories in that time," says Akhlesh Lakhtakia.

It is an unusual claim from someone in his job. Lakhtakia is not an astronomer, but an electrical engineer based at Penn State University in University Park, Pennsylvania. Nonetheless, working with Tom Mackay, a mathematician at the University of Edinburgh in the UK, he has now published a string of peer-reviewed papers showing that some of our astronomical observations really could be wrong. They have demonstrated that our cherished night sky could be replete with optical illusions created by the gravitational fields of black holes.

The significance of their work remains controversial, but it could be revolutionary. Understanding these illusions could lay bare the composition of the universe, the existence of wormholes and extra dimensions - even the very nature of space and time.

The story began three years ago when Mackay and Lakhtakia started working together on a phenomenon called negative refraction. Light travelling through air bends, or refracts, when it passes into other materials such as water or glass. This is because light travels at different speeds in water and air, and the amount of refraction depends on this speed difference. Every known material slows light relative to its speed in a vacuum, and it always bends in the same direction.

But in 1967, a Russian physicist called Victor Veselago came up with the idea of a material that bends light the other way. Veselago modified Maxwell's equations, which describe how electromagnetic waves travel through materials, and showed it should be possible to create a material that would bend light in the opposite direction.

Veselago's material remained a flight of fancy for over three decades. Then, in 2000, physicists announced that they had at last created a composite material that produced negative refraction. It was an array of wires and copper crescents, and worked at microwave frequencies. Signals flowing through this strange composite behaved as though they were speeded up, not slowed down, and bent the opposite way to normal.

This innovation has huge potential. Adapting it to work at visible wavelengths could lead to "perfect" lenses capable of focusing on details hundreds of times smaller than conventional lenses can. Such lenses would be a huge boon to computer chip manufacturers, who are desperate to squeeze ever more components onto ever smaller circuits. No wonder armies of electrical engineers have been trying to create more of these negative refraction materials, piecing together ever-smaller arrays in the hope that they will eventually work at wavelengths small enough to bend visible light the wrong way (New Scientist, 14 April 2001, p 35).

But Lakhtakia and Mackay decided not to follow the crowd. "Everyone was trying to do it on smaller and smaller things, creating nanostructures with negative refraction properties," he says. "But I knew it should also be found on large length scales - so we decided to go the other way." Since the laws of electromagnetism are the same at all scales, Lakhtakia thought the best test of negative refraction might be to see whether space itself could produce the effect.

To test their idea, the pair had to get to grips with general relativity, Einstein's description of the way gravity affects light's path through the cosmos. This theory tells us that space can affect the path of light, because mass and energy distort space and time, creating warps and dents that we call gravity. This is the basis of gravitational lensing, in which light from distant galaxies can be deflected on its way to Earth by the gravitational field of some massive object that lies in the way. Because of this we see the galaxy distorted into an arc or halo, or even multiple separate images.

But could gravity's distortion ever create negative refraction? Not wanting to reinvent the wheel, Lakhtakia and Mackay began to search through the literature, and found that Igor Tamm, a Russian physicist who shared the Nobel prize in 1958 for the discovery of Cherenkov radiation, had already suggested that curved space-time might create curious conditions for electromagnetism.

In the late 1920s Tamm found a way to simplify the description of how electromagnetic waves move through a space-time warped by the myriad dimples made by stars and galaxies. According to Tamm, it is exactly equivalent to moving through a non-warped space-time - but in a very strange, imaginary "bi-anisotropic" material. That material affects the electric and magnetic components of an electromagnetic wave in different ways, and its effect also depends on the direction in which the wave is moving through the material.

The way that bi-anisotropic materials handle electromagnetic waves gives scope for negative refraction effects. So Mackay and Lakhtakia worked out the conditions in which the material would create negative refraction (Journal of Physics A, vol 37, p 5697), and set about finding where in the universe these conditions might occur.

They began by searching through the cosmology literature for examples of relativistic equations and solutions that matched the results they had derived, trying to pin down what the equations were saying in terms of astrophysical phenomena - an arduous task for people who normally read engineering journals. But by August last year Mackay and Lakhtakia were convinced they had found what they were looking for.

They discovered that the equations describing the region near a rotating black hole bear a striking similarity to those for materials that produce negative refraction. Of course gravity is so strong inside a black hole that nothing, not even light, escapes. But just outside this horizon of no return lies a zone called the ergosphere, where energy and matter can still escape being sucked into the black hole. So the extreme distortion that a spinning black hole creates in Einstein's space-time seems to provide the right conditions to bend light in the opposite way to that which you would normally expect.

Mackay and Lakhtakia are quick to point out that there is not yet any evidence that negative refraction actually occurs in space. But that doesn't mean it is not happening; after all, there are a million black holes in our galaxy alone, and almost all of them are thought to be rotating.

Other astronomical objects may also create a similar effect. "I would think black holes aren't the only objects that could cause this phenomenon," Lakhtakia says. So far the only other type of space-time distortion they have looked at is that caused by an inflating universe - and they found it also creates conditions for negative refraction. Massive stars might create similar conditions, and the researchers are investigating other possibilities too. "We are looking at charged black holes now and I think we will see the same thing there," he says. "The phenomenon is not likely to be uncommon."

Lakhtakia thinks negative refraction might be observed in the same way as gravitational lensing, although perhaps not for a while - he simply doesn't know where to start. "There are no candidates that I know of," he says. "But I don't know enough. I'm not an astrophysicist." Not that astrophysicists would necessarily know where to start, either: their observations of the universe already present them with puzzling phenomena. And negative refraction could confuse the picture even more.

Dark matter, for example, is a serious headache. When astronomers measure the mass and spin rate of rotating galaxies, they find that the gravitational attraction between all the matter in the galaxies is not strong enough to hold them together; the centrifugal force should tear them apart.

Researchers have come up with two ways to explain this. By far the most popular solution is to suggest that the galaxies are shrouded in invisible "dark matter" that provides the required gravitational top-up. The other answer is that we haven't understood gravity properly, and some modification to its laws at galactic scales would explain the anomaly.

Skewed stars

Mackay and Lakhtakia now offer two more options. First, that the stuff we see in the galaxies may not be where we think it is: rotating black holes in our line of sight may be causing negative refraction and skewing all our measurements of stellar positions (see Diagram). Reinterpret the distribution of the matter within the galaxies through the prism of negative refraction and maybe the dark matter problem will go away, they suggest.

The second option is that the dark matter itself could cause negative refraction. "If light is observed to undergo negative refraction in a region of apparently empty space-time, then we may infer that there is dark matter acting. We may also be able to infer something about the nature of the dark matter," Mackay says.

These are speculative and controversial ideas, but the dark matter problem is far from resolved, and the distortion of starlight is certainly at the centre of the controversy. Some gravitational lensing observations, for example, suggest that either we have underestimated the age of the universe by 6 billion years, or we have to accept that we have completely misunderstood dark matter and how it is distributed in galaxies (New Scientist, 13 November 2004, p 42). Another set of lensing surveys have produced conflicting results about the very nature of dark matter (New Scientist, 16 April, p 10).

Negative refraction might also have a bearing on another area of cosmology: the existence—or otherwise—of dark energy and hidden extra dimensions of space. Lakhtakia and Mackay have shown that the phenomenon of negative refraction is linked to something called the cosmological constant (The European Physical Journal C, DOI: 10.1140/epjcd/s2005-01-001-9). Einstein first included this constant in his description of space-time because he believed the universe was meant to be static - neither expanding nor contracting. Only by putting a positive constant into his equations could he make them describe a static universe. Without it, the universe's expansion would slow down, stop and eventually reverse.

Einstein later referred to this fudge factor as his "biggest blunder", after observations made by Edwin Hubble revealed that the universe is not static, but is expanding. What's more, recent observations of distant supernovae indicate that something is accelerating that expansion. Cosmologists suggest this expansion is caused by a "dark energy" that permeates the universe, corresponding to a small, positive value for the cosmological constant.

According to the supernova results, the dark energy causing the acceleration accounts for 73 per cent of all the energy in the universe. But this stretches the credulity of some physicists, who argue that we can't be sure that the universe's expansion is really accelerating. The evidence is scant, they say, and the cosmological constant could still be zero, or even negative. That latter possibility is borne out by "brane-world" models of the universe, where the three dimensions of space we experience are just part of a multidimensional reality. In these models the cosmological constant can be either positive or negative.

Lakhtakia and Mackay might have found a way to help. Based on a description of space-time developed in the 1970s by Stephen Hawking and Gary Gibbons at the University of Cambridge, they have shown that negative refraction is only consistent with a universe that has a positive cosmological constant. So seeing a star in the wrong place might do more than shed some light on dark energy: if astronomers find evidence of negative refraction away from the vicinity of a rotating black hole, it will confirm that the universe's expansion is indeed accelerating. It might also rule out some of the brane-world models. Not bad for an idea born from electrical engineering.

Of course, all this hinges on someone finding a concrete example of a star that appears out of place because of negative refraction. Lakhtakia and Mackay are now appealing to astrophysicists to have another look at their observations, to see if there are any clues worth following up.

On the surface, it looks promising. "The ergosphere of a black hole is a very peculiar place where many physical phenomena go against our intuition," says Serguei Komissarov, a cosmologist based at the University of Leeds in the UK. "The idea that some electromagnetic waves can suffer negative refraction within the ergosphere is not that crazy." But, he adds, he would need to study the issue in detail to know whether there were really interesting astrophysical implications.

Christopher Kochanek, an astronomer based at Ohio State University in Columbus, doesn't think it would be worth the effort; researchers already take these issues into account, he says. He points out that cosmologists routinely use the equations of general relativity to compute photon trajectories through the universe - including the regions around rotating black holes. "Remember that in all of this there is no change in how electromagnetism works or how you calculate photon trajectories," Kochanek says. "It may be interesting to phrase some of the astrophysical stuff in terms of a negative refraction, but it doesn't actually change how you compute anything."

Lakhtakia thinks he's seen this kind of scepticism before, however. "Technically the astrophysicists are right: they take ergospheres into account," he says. But he worries that astrophysicists may be throwing away important information. For example, until five years ago, researchers using Maxwell's equations to calculate the path of light through materials routinely discarded results that lead to a negative refraction. "After all, who had ever heard of negative refraction?" Lakhtakia says. "Astrophysicists are building in all sorts of assumptions based on the current state of knowledge. People discard results that do not fit into their experience."

But Alexei Starobinsky, a cosmologist based at the Landau Institute for Theoretical Physics in Moscow, has a more fundamental objection. He points out that black holes capable of producing these kinds of effects constitute a negligible part of the whole sky. Mackay agrees, but he says that doesn't mean their contribution must be negligible. "Their effects are definitely considered as spectacular. Even tiny effects are amplified by astronomical distances." There is also the negative refraction that could be caused by the inflating universe to consider. And things get even more interesting if dark matter is composed of black holes, as some cosmologists suspect. "If this is the case then the negative refraction effect contributed by these black holes may be substantial," Mackay says.

Mackay, Lakhtakia and Sandi Setiawan, a mathematician who has begun working with Mackay in Edinburgh, are aware they are treading on toes, but they also think the astronomers are assuming too much. "We are neither astronomers nor astrophysicists," Mackay says. "However, those two groups of scientists have not 'seen' or 'explained' everything. We know the human race is largely ignorant of what happens in outer space."

Until astronomers re-examine the solutions to Einstein's equations that they have hitherto ignored, we cannot be sure that we haven't misunderstood what the stars are telling us, Lakhtakia says. "The situation with negative refraction in space is extraordinarily complicated, and our best inputs are going to come from people who will keep an open mind. These are speculations on our part, but then much of astrophysics is speculation."