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A Daring Journey

Travel to a land just over the horizon, where time slows down and you can stretch out and take it easy. It's the perfect vacation spot -- if you like black holes.

by Gregory A. Shields

StarDate magazine mar/Apr 2003 coverAmong the bizarre phenomena of astrophysics, perhaps none fascinates more than the black hole. Matter compressed to such a density that only its gravity remains part of our universe? Crushing gravitational forces, strange distortions of space and time, wormholes into another universe? No wonder school children and seasoned astronomers share a sense of wonder at the idea of black holes.

All this interest centers on a kind of object that, in a sense, can never be seen. To see something, we must receive light from it, and a black hole is by definition a region of space where gravity is so strong that not even light can escape.

Isaac Newton's theory of gravity led to early concepts of a black hole in the late 1700s. Gravity's pull on an object grows weaker as the distance increases. If a space probe or other projectile is launched from the surface of a massive body with sufficient speed, it will fly off into space forever. This minimum speed is called the escape velocity.

In Newtonian gravity, the escape velocity from a spherical body depends on its size and mass. As the size decreases and the mass increases, escape velocity goes up. For the escape velocity to equal the speed of light (186,000 miles (299,000 km) per second), nature requires a certain size for a given mass. If an object contracts to this critical size, light can no longer escape from its surface to the distant universe. This is the essence of a black hole.

The modern concept of a black hole is rooted in Albert Einstein's 1915 theory of gravity, called General Relativity. In 1905, Einstein's theory of Special Relativity had showed that space and time are affected by the motion of the observer. In 1908, Hermann Minkowski interpreted these effects in terms of a unified four dimensional spacetime -- a universe in which the three dimensions of space and the fourth dimension of time are interconnected. General Relativity then explained gravity as a curvature in spacetime caused by the presence of matter. The curvature affects the motion of objects traveling through spacetime, and we experience these effects as gravity.

In 1916, German astronomer Karl Schwarzschild solved the equations of General Relativity to describe gravity around a spherical mass. His calculations showed that if the mass is contained within a critical radius, light cannot escape to the outside universe. This radius is now called the Schwarzschild radius, and it marks the "edge" of a black hole.

Astronomers confirmed Einstein's theory in 1919 by observing a solar eclipse. General Relativity predicts that the gravity of a massive object, like the Sun, should "bend" the light of more distant objects. During the eclipse, as the Moon covered the Sun, astronomers measured the positions of stars that appeared close to the Sun. As Einstein predicted, the positions of these stars were shifted just a bit -- the result of the Sun's gravity warping the space around it.

The concept of a black hole was now on a firm footing, although the term "black hole" wasn't coined until 1968, by American physicist John Wheeler.

When we think of a black hole, our thoughts naturally focus on the Schwarzschild radius, also called the horizon or event horizon of the black hole. Anything inside this horizon is lost to the outside universe.

The gravity of a black hole extends far beyond the horizon, though. At great distances, the effects resemble those of "normal" objects, like stars and planets. (If our Sun were suddenly squeezed enough to become a black hole -- a physical impossibility, by the way -- Earth would continue to orbit at its current distance, and would not be "sucked in" by its gravity.) Only very close to the horizon -- a few times the black hole's radius -- do the effects of General Relativity become extreme.

What phenomena would we experience if we could journey to the vicinity of a black hole in our Milky Way galaxy?

If the black hole is 10 times as massive as the Sun, as might be formed when a massive star explodes, the diameter of the horizon is about 40 miles (60 km), the size of a large city. If we explore at distances much larger than this, say 6,000 miles (10,000 km) or more, the hole's gravity will behave like that of any other object, like a "normal" star or a planet. We can measure the black hole's mass by finding the speed we must maintain to remain in a circular orbit around it.

Once we attain that speed, we can safely orbit the black hole and watch both the hole and its surroundings. As we orbit the hole, for example, we see it pass in front of the background stars. As the black hole approaches, stars in its path appear to move aside, returning to their normal positions when the hole has passed. This is the phenomenon of gravitational lensing, caused by the bending of light as it passes near a massive body (the same effect observed in the 1919 eclipse). The displaced star images outline a ring around the black hole.

Our discussion has neglected a practical detail, however.

As we approach the black hole from far away, we become aware of the effect of the black hole's gravity on our own bodies. If we decide to stop at some distance away from the hole and make observations, we must fire our rocket engines to oppose the pull of the hole's gravity. But we would need so much thrust that it would crush us inside the spacecraft when we were still quite far from the hole.

We can obtain temporary relief by turning off our engines and falling freely toward the hole, or orbiting around it. However, when we come within a few thousand miles of the hole, the so-called tidal gravitational force of the hole becomes uncomfortable. (This is the same force that creates ocean tides here on Earth.) If we're falling feet first into the black hole, it pulls harder on our feet than our head, which stretches our bodies lengthwise. At the same time, gravity squeezes us in both sideways directions. As we continue our fall, we're soon destroyed by the tidal gravity.

To continue our journey to the black hole, we must imagine ourselves as indestructible, so that the tidal forces do not affect us. Separating from our mothership, we drop down to a distance of about 200 miles (300 km), or 10 times the radius of the black hole. Hovering here with the aid of our rocket engines, we perform some experiments with rugged equipment that is not affected by the gravitational forces. Our atomic clock is running normally, and all other physical processes appear to behave normally. Our radio transmits waves with the normal frequency and wavelength, and our lasers produce light of the normal color. The speed of light has its normal value. We transmit a message back to the mothership that has wisely stayed far from the hole, saying, "What's all this talk about distortions of space and time near a black hole?"

Watching through a powerful telescope, our colleagues on the mothership see that we have attempted to send a radio message.  However, tuning their receiver to the normal transmission frequency of 100 megaHertz, they hear nothing. Only by tuning to a lower frequency of 95 megaHertz do they receive our message.

Scrutinizing our ship through the telescope, they see our clocks running too slow, by the same proportion. As the clock on the mothership ticks off 100 seconds, they see our clock near the black hole advance by only 95 seconds. This phenomenon is called time dilation, in which time seems normal to observers in both locations, but periodic signals slow down as they move away from a source near a black hole (or any massive body). Because radio waves or light waves are periodic (they repeat themselves), their oscillations are slowed down by the same factor as for the ticks of a clock. This is called the gravitational redshift, because a decrease in frequency corresponds to a shift toward longer, "redder" wavelengths. Strong gravity does indeed affect the time near a massive body as perceived by an observer far away.

The gravity of a black hole affects space as well as time, as we discover if we test the relationship between the circumference and radius of a circle centered on the hole. Of course, we can't stretch a measuring tape from our location to the center of the black hole, because it would be yanked into the hole as soon as it crossed the horizon. However, we can measure the circumference of a circle at our own location by laying down yardsticks all around the circle, or by timing a ray of light that's reflected around the circle by a set of mirrors. Then we move one kilometer closer to the hole, and measure the circumference there.

Normal Euclidean geometry says that the difference in circumference must be exactly 2pi times the difference in radius, so we expect the circumference of the smaller circle to be 6.28 kilometers less than the circumference of the larger one. Our measurements, however, show that the difference in circumference is actually only 5.96 kilometers. The curvature of spacetime has altered the normal laws of geometry.

If we drop progressively closer to the horizon, these phenomena become more extreme. Circumferences change less and less for a given difference in radius. The distant mothership sees our clock running ever slower, and the blue light on our control panel appears green, then yellow, and then red. As we approach the horizon, colleagues on the mothership see us become very red and dim, and then disappear. The outside world can never see an object cross the horizon of a black hole.

We can, however, volunteer for a suicide mission to enter the black hole. If we stop our rocket engines and go into free fall, the laws of physics within the small confines of our probe remain normal. If we don't look out the window of our craft, we will only know we're approaching the horizon because of the strengthening tidal gravitational forces. When we cross the horizon, we feel no jolt. Local physics remains normal, and the tidal forces show no sudden increase. However, now we are doomed to fall into the singularity -- the ultradense pinpoint at the center of a black hole that contains all of its mass -- in a fraction of a second, no matter how powerful our rocket engines are.

So far, we have described black holes of a size that would be formed in the death of a massive star. However, much larger black holes, millions or billions times as massive as the Sun, appear to inhabit the centers of many galaxies, including the Milky Way. How would our experiences differ near such a hole?  Many of the phenomena, such as lensing, time dilation, gravitational redshift, and geometrical effects, depend on our distance from the black hole divided by its size.

However, the tidal forces are weaker near the horizon of a larger hole. For supermassive black holes, we would not even notice the tidal forces as we fell through the horizon, although the forces required to hover near the horizon would still be crushing.

Does any of this really happen in our universe? General Relativity says that when enough matter is compressed into a small radius, a black hole will form. Relativity has been verified in a variety of ways. The gravitational redshift has been observed in studies of white dwarf stars as well as experiments here on Earth. The bending of light by the Sun's gravity has been verified by solar eclipse studies, radio transmissions from spacecraft, and observations of distant galaxies and quasars.

Theories of stellar evolution predict that black holes or neutron stars will form when the heaviest stars die, and we have discovered many neutron stars throughout the galaxy. Fundamental theoretical arguments say that a neutron star cannot be more than about three times as massive as the Sun. We see binary X-ray stars in our galaxy, in which the X-ray source is so small that it must be a neutron star or black hole. Where the mass of this object is too great to be a neutron star, a black hole is the only remaining alternative.

In the centers of the Milky Way and other galaxies, the rapid motions of stars and gas clouds close to the galactic center betray the presence of a dark object of enormous mass and tiny size. In some cases, a black hole is the only viable possibility. And the small size and tremendous power of quasars calls for enormous disks of hot gas orbiting supermassive black holes. The evidence is strong that black holes exist, and the properties of black holes are clear consequences of General Relativity.

Most astronomers accept the existence of black holes. The challenge today is to find them, measure them, and improve our observations of the phenomena associated with them. We may have met nature's most bizarre phenomenon. Now it's time to get better acquainted.

Gregory A. Shields is the Jane and Roland Blumberg Centennial Professor in Astronomy at The University of Texas at Austin.