Like a giant pale blue eye, the Earth stares at the centre of our galaxy. Through the glare and the fog it is trying to catch a glimpse of an indistinct something 30,000 light years away. Over there, within the sparkling starscape of the galaxy's core... no, not those giant suns or those colliding gas clouds; not the gamma-ray glow of annihilating antimatter. No, right there in the very centre, inside that swirling nebula of doomed matter, could that be just a hint of a shadow?

The shadow we're straining to see is that of a monstrous black hole, a place where gravity rules supreme, swallowing light and stretching the fabric of space to breaking point. Black holes are perhaps the most outrageous prediction of science, and even though we can paint fine theoretical pictures of them and point to evidence for many objects that seem to be black hole-ish, nobody has ever actually seen one.

All that could change in the next few months. Astronomers are working to tie together a network of microwave telescopes across the planet to make a single instrument with the most acute vision yet. They will turn this giant eye towards what they believe is a supermassive black hole at the centre of our galaxy, code name Sagittarius A* (see image).

Even part-built, the microwave eye has already produced a hazy picture of Sagittarius A*. Last September, a team led by Shep Doeleman of the Massachusetts Institute of Technology's Haystack Observatory in Westford published results that are almost good enough to show the reputed black hole (Nature, vol 455, p 78).

Soon, Doeleman and his team hope to see the hole's dark silhouette. Then they want to watch matter falling into it in order to trace out the twisted space-time around the black hole. That could tell us how it formed and grew.

These observations will also be the sternest test yet of Einstein's general theory of relativity, which predicts the existence of black holes. If relativity breaks down, Doeleman and his team might not see a black hole at all, but something even stranger.

What we do know for sure is that something big lurks at the centre of our galaxy - because its powerful gravity affects the motion of nearby stars and gas. That something is about 4.5 million times the mass of the sun and crammed into an area the size of the inner solar system. There are few obvious ways to pack stuff in so tightly. Four million suns would be a dead giveaway, for instance. A swarm of neutron stars or small black holes would be highly unstable. So our best bet is one massive black hole.

A supermassive black hole is thought to sit at the centre of most large galaxies. In some so-called active galaxies, enormous quantities of gas are swirling into the black hole, forming a disc of hot matter around it that often outshines the billions of surrounding stars.

Our own galactic monster is less well fed, surviving on only a thin gruel of gas streaming out from nearby stars. As this gas falls towards the hole it also heats up and shines, though more faintly than the disc in an active galaxy. All kinds of electromagnetic radiation are emitted, ranging from radio to X-rays (see image).

Of course, the black hole itself does not shine since it actually swallows light. That is how we hope to be able to see it: light from gas swirling round the hole will be devoured, so the hole should show up as a shadow or silhouette against the background of hot, shining gas.

Seeing this shadow is not easy. It won't have sharp edges because we will still see light and other radiation from gas in front of the hole. It will also look very small. According to relativity, a black hole of 4.5 million solar masses should be 27 million kilometres across, and even though its gravity warps nearby light rays, making it appear about twice that size it will still seem very small. From our distant viewpoint halfway across the galaxy, that would cover an angle of only about 50 micro-arcseconds - the size a football would appear on the moon, or a small bacterium held at arm's length.

No ordinary telescope could see such a small dark smudge. Instead, Doeleman is using a well-tested technique called very long baseline interferometry or VLBI. By combining the observations from widely separated dishes across the planet, radio astronomers can effectively reconstruct what would be seen by one enormous dish - even one as large as the Earth. Because small dishes collect less light, a VLBI image is less bright than the image from a real planet-sized dish would be, but it can reveal just as much detail.

Previous VLBI observations of the galactic centre have been far too fuzzy to see the black hole's shadow. For starters, we are peering right through the most crowded parts of the galaxy, where lots of gas scatters radio waves. "It is like dense fog blurring the image of a streetlight," says astrophysicist Avi Loeb of Harvard University.

Worse still, the gas swirling around the black hole is opaque to most wavelengths, throwing a veil over the shadow. And more fundamentally, the resolution depends on the wavelength of radiation being observed, with long waves giving us a vaguer picture than short waves.

Luckily, all of these problems go away if your telescope works at wavelengths of about 1 millimetre. Such short-wavelength radiation cuts through the interstellar fog and the inner veil of gas. Also, the resolution for a telescope with dishes separated by thousands of kilometres is just about fine enough, in theory, to see the shadow. In fact the bigger the dish separation, the better.

Doeleman's team adapted VLBI to work at the ultra-short wavelength of 1.3 millimetres. In April 2007 they took their hardware to mountaintop telescopes in Arizona, California and Hawaii.

See the CARMA telescope in California and the James Clerk Maxwell Telescope in Hawaii

The result was frustrating. They did pick up emissions from the central region of Sagittarius A*, but they don't quite have enough information to get an unambiguous picture of it. "We have two models that fit the data," says Doeleman. In one, Sag A* looks like a doughnut with a hole in the middle, which may be the supermassive black hole. Unfortunately their observations also fit a simple blob of bright emissions, with no apparent black hole shadow.

Even so, these early observations are a strong sign that Sag A* really is a black hole. According to Avery Broderick at the University of Toronto, Canada, the results indicate that it almost certainly has an event horizon, the defining feature of black holes.

An event horizon is an insubstantial boundary, within which nothing can escape the grip of the black hole's gravity. Matter crossing a horizon just gets quietly swallowed, emitting no radiation. Some theoretical alternatives to black holes, such as the giant balls of lightweight particles called boson stars, would have physical surfaces instead of horizons. These surfaces would be warmed by gas falling onto them, with the smallest ones heating up the most.

Along with Loeb and Ramesh Narayan at Harvard, Broderick has analysed Doeleman's results and argues that if Sag A* had a surface it would be hot enough to glow with a steady emission of infrared light. In fact, no such glow has been detected. They conclude that an event horizon does cloak Sag A*, cutting us and the rest of the universe off from whatever lies within.

Still, there may be loopholes in this argument so it would be better to actually see the hole for ourselves. In April, Doeleman returned to Hawaii. To try to boost sensitivity, he decided to try to use the signals from three telescopes rigged together on Mauna Kea instead of just one. "I think we've shown we can do that tonight," he told me from the summit on 3 April. After some months of processing, this latest set of observations ought to finally reveal the shadow of the monster.

Black hole: the Movie

That first faint smudge will only be a beginning. Doeleman wants to move to an even shorter, sharper wavelength of 0.87 millimetres. Meanwhile, more and more telescopes will be brought together to get a more revealing view of the black hole.

The centre of Earth's microwave eye will be in the mountain deserts of Chile, where the Atacama Large Millimeter/Submillimeter Array (ALMA) is being built (see image). All of its 66 dishes should be up and running by 2012. "ALMA will be the new 800-pound gorilla on the block," says Doeleman. In concert with other scopes across the planet, it should provide a much sharper picture of Sag A*, as well as revealing an even bigger black hole in the galaxy M87.

It could also give us "black hole: the movie". "What I'm most excited about is that we can look for temporal variations," says Doeleman. Observations made at many wavelengths have revealed sudden outbursts of radiation from the gas swirling around Sag A*. Using VLBI, Doeleman wants to watch these small flares circling and being swallowed by the horizon in real time. "That's the money-shot in this business," he says.

It could reveal something researchers would dearly love to know about black holes: their spin. Relativity says that a spinning black hole will form a whirlpool in the fabric of space, a phenomenon known as frame dragging. Hotspots close to the hole would be caught in this whirlpool, so their motion will show how fast Sag A* spins. That in turn will give us a hint about the black hole's past life, because its spin depends on what it consumed to become the heavyweight it is today.

Emanuele Berti of the University of Mississippi in Oxford and Marta Volonteri of the University of Michigan in Ann Arbor have calculated the effects of a few different diets. Sag A* might have grown up on a steady diet of galactic gas. Sharing the overall rotation of the galaxy, that gas would form a disc spiralling faster and faster as it approaches the hole, like water going down a plughole. When the gas is finally swallowed, its spin would add to that of the hole. If Sag A* put on most of its weight that way, its spin would be boosted close to the maximum possible value relativity allows.

Or perhaps Sag A* grew up by snacking on gas from a host of nearby sources in random orbits. The randomly oriented spins of those snacks would mainly cancel each other out, so the spin of Sag A* would probably be low.

Another possibility is that Sag A* grew hierarchically, as smaller galaxies merged to form the Milky Way. Each galaxy would have brought its own massive black hole and they would all have merged together to form Sag A*. In Berti and Volonteri's simulation, that usually adds up to a hole with moderate spin.

Of course, all of this assumes that Einstein's general theory of relativity holds true. Almost a century after he devised it, general relativity remains our best theory of gravity and matches precise observations of planetary orbits and gravitational lensing. "It's almost embarrassing how good general relativity is," says Broderick. But the theory has never been tested in the super-strong gravity near a black hole, where its predictions are most extreme. Broderick wants to make amends by following the motion of hotspots through this warped and twisted space. "The best way would be to place an undergraduate at the galactic centre with a laser pointer," he says. "But if these flares do happen we can use them instead."

By mapping out the exact shape of space-time near the hole, the flare movie could distinguish between relativity and some competing theories developed to explain the anomalous motions of stars and galaxies more commonly attributed to dark matter and dark energy. Among them are complex theoretical schemes known as scalar-tensor-vector gravity and f(R) gravity.

And what if Doeleman's latest observations, made last month, show something odd? Could the horizon be a strange shape? Or not show up at all? "Then we would have a problem," says Broderick. It could mean the relativity is radically wrong when it comes to super-strong gravity. And the monster at the centre of the galaxy will be even more shadowy than we thought.

Other black holes worth viewing

Our galactic centre is not the only target for astronomers trying to image black holes. In a galaxy called M87 there is a truly vast black hole, more than 3 billion times the mass of the sun. Radio astronomers hope to be able to zoom in on this monster, not only to see the dark shadow of the hole's event horizon, but also to find the origin of a gigantic jet of matter squirting out of M87.

See M87 in X-ray and radio light and in a composite Hubble image

At about 60 million light years away, M87 is 2000 times as far away as Sagittarius A*, the black hole in the centre of our galaxy. So even though it is several hundred times the diameter of Sag A*, M87's black hole appears about one-third of the size. At the moment, that means we cannot see it clearly even with an astronomical technique called very long baseline interferometry (VLBI), which links many radio telescopes to create a giant virtual scope.

All that will change as the Atacama Large Millimeter/Submillimeter Array in Chile comes online over the next few years. "That will bring M87 in range of our VLBI artillery," says astronomer Shep Doeleman of the Massachusetts Institute of Technology in Westford.

The next two black hole candidates are in the Sombrero galaxy and Centaurus A, 30 million and 12 million light years away respectively. Their shadows will appear even smaller than the hole in M87 and might be beyond the power of Earth-based radio astronomy to resolve.

One day a rather different instrument could give us sharp pictures of these black holes too. A proposed space mission called Black Hole Imager would use X-rays instead of radio waves. Two or more X-ray telescopes flying in formation could in theory provide sufficient resolution.

The mission is only in the early stages of discussion and won't fly for decades. "It is possible by 2030, but that requires an aggressive technology development programme," says astronomer Keith Gondreau of NASA's Goddard Space Flight Center in Greenbelt, Maryland.