1. Imagine a Black Hole...

Gravity is pretty much all you need to think about to imagine a black hole. In essence a black hole is gravity gone mad. The classic one line definition of a black hole goes something like this:

"A black hole is a region of space where gravity is so strong that nothing, not even light, can escape."
But this really does not do justice to how strange and wonderful black holes can be.

1.1 The pull of gravity

Gravity acts as an attractive force; it keeps us rooted to the Earth and it keeps the Earth in orbit around the Sun. The Earth's gravity is so effective at keeping us on the ground that it takes a considerable effort to escape! If you throw a stone up in the air it will undoubtedly fall back down to Earth regardless of how hard you throw it. In order to get the stone to escape the Earth's gravity and fly off into space you would need to throw it at a speed of more than 11,200 meters per second (24,840 miles per hour). This the the escape velocity, i.e. the speed required for an object to leave the Earth's surface and not be pulled back down by gravity. The escape velocity of an object (such as a planet or star) is the speed with which you need to be launched in order to leave the surface and permanently escape the object's gravity.

The escape velocity of a planet depends on the mass of the planet (how much matter it is made of) and also on its size (radius). Jupiter is by far the most massive planet in the solar system and it has the largest escape velocity. If you were near the surface of Jupiter you would need to throw a stone at more than 59,000 meters per second (133,875 mph) for it to escape Jupiter for good.

For a star or planet of given mass, a smaller size leads to a higher escape velocity. This is easy to understand because the smaller the size, the closer the surface is to the centre of gravity and the stronger the pull of gravity is there.

1.2 The first dark stars

In 1783 John Michell (1724-1793), a natural philosopher, presented a paper to the Royal Society in which he predicted the appearance of a very massive star (one with very high mass). The escape velocity from the surface of a star is higher for more massive stars because of the stronger surface gravity. The escape velocity of Michell's hypothetical massive star must therefore be high.

In particular, Michell calculated the gravity from a star that was 500 times the radius of the Sun, but the same density. (This means it has 125 million times the volume, and therefore 125 millions times the mass, of our Sun.) He calculated the escape velocity from the surface of this gigantic star and found it to be in excess of the speed of light! He reasoned that any light emitted from the surface would not be able to escape the surface of the star - the star would appear black to an outside observer. He supposed there might be a huge amount of "dark stars" in the Universe.

"If the semi-diameter of a sphere of the same density as the Sun in the proportion of five hundred to one, and by supposing light to be attracted by the same force in proportion to its [mass] with other bodies, all light emitted from such a body would be made to return towards it, by its own proper gravity."
The other way to imagine a dark star is to think what would happen if you could take a normal-sized star like the Sun and shrink it down (compress it to make it much denser). As the star gets smaller its escape velocity increases - the mass stays the same but by squashing the star the surface gets closer to the centre of gravity, so the effect of gravity increases. Eventually the star is so compact that its escape velocity is the speed of light. If the star becomes even more compact then its escape velocity will be higher than the speed of light. In order to leave the surface of the star and escape the star's gravity, one would need to move faster than the speed of light!

1.3 Einstein's idea

Einstien Michell's idea of a dark star is a very interesting one but based on the old ideas about gravity and light that Newton had set down in the 17th century. It turns out these are not accurate for describing such compact stars (although in the more 'normal' environment of our Solar system they are very accurate). By 1900 it was obvious there was more to gravity (and light) than Newton had described. Only when Albert Einstein [1879-1955] published his theory of gravity - called general relativity - did it become possible to try and answer the question of what a very compact star might look like.

Einstein's great theories come from remarkably simple beginnings. His first theory of relativity - special relativity (so-called because it only applies in special circumstances), published in 1905 - came from the fact that the speed of light in a vacuum is constant no matter how you happen to be moving. This is a rather alarming fact when you think about it. Imagine travelling in a spaceship at almost the speed of light (99% say) and turning on the headlights, what would happen to the light? Hard to imagine as it is, it turns out the answer is that the light shoots out of the headlights at 100% the speed of light, apparently just as it would if you were stationary! (The first experiment that demonstrated this fact was performed in 1881 by Albert Michelson [1852-1931] and Edward Morely [1838-1923]; click here or here for more information.) In order to get this bizaar fact to make sense Einstein had to start re-building physics from the bottom up. In order to explain gravity properly, taking into account his new ideas, he needed a more general theory. This became Einstein's theory of gravity: general relativity, first published in 1915.

The starting point is: acceleration vs. gravity. When you have been a lift (elevator) you have probably felt a force acting on you as the lift accelerated. As the lift accelerates upwards it feels like there's a force pulling you down. It feels like you've got a bit heavier, or like gravity got stronger. As the lift decelerates (or accelerates downwards) you feel the opposite force, you feel lighter. Most of us never give this a second thought, but to Einstein this was the starting point for a revolutionary new theory.

Let's do a thought experiment. Imagine yourself in a lift that has been blasted off the Earth on a rocket and is now lost somewhere in deep space. (Obviously the lift has some sort of life-support system in it!) The lift does not have any windows.


Priciple of equivalence

Initially you are weightless, floating around inside the lift. Far away from all planets and stars there is no pull of gravity and so you feel no weight pulling on you. Nice and relaxed you fall asleep. When you wake up you are lying on the floor of the elevator and feel a force pulling you to the floor. You feel about as heavy as you did on Earth. (You have got your weight back!) The obvious possibility is that the lift has somehow drifted back to Earth and it's Earth's gravity you can feel pulling your feet to the floor. Or maybe the lift has started accelerating at one "g-force" and it's the force from the acceleration that's keeping you on the ground. How can you tell?

It is not obvious whether it is possible to tell the difference between the two possibilities: (i) accelerating in free space and (ii) at rest on the Earth (see the image on the left). Maybe it's not possible to tell the difference!? maybe there is no difference...?

Einstein followed the implications of the idea that the force of gravity (when you are at rest) is the same as the force due to acceleration (when you are in free space) - called the principle of equivalence - to it's logical conclusion and in the process formulated a complete, new theory of gravity!

His theory of general relativity is really all geometry. Einstein explained gravity in terms of the geometry of spacetime. We shall not concern ourselves with this too much. His theory of "warped spacetime" is highly mathematical but we can review some of the important results quickly.


1.4 Light gets bent!

accelating lifts One result of Einstein's theory is that light should be bent by gravity. We normally think of light as moving in straight lines but this is not so according to Einstein. The path of light rays should be bent slightly as they pass a massive object like a star. To see how this comes about let us go back to those strange lifts again, only now we shall give them windows.

I am in the accelerating lift. You are in a spaceship watching the lift accelerate towards you. As I draw level with you, you fire a laser beam at me through the window! Obviously the laser beam will move in a straight line at the speed of light. So, as the lift's window becomes level with your spaceship you fire the laser beam in through the near-side window.

The laser beam goes in the window but doesn't reappear through the opposite window. It took the laser beam a tiny fraction of a second to get from one side of the lift to the other. (Remember, although light is fast it is not infinitely fast so it does take a small amount of time to get from one side to the other.) In this time the lift had moved on a bit, the laser beam missed the far window. The lift was continuing to accelerate as the light beam entered the near window. In the time it took the laser beam to get from one window to the other the lift had moved on, so had the window, and the laser missed the far side window.

Now imagine the situation from my point of view: inside the accelerating lift as you shoot at me from the spaceship. From this point of view the laser beam doesn't look like it's moving in a straight line. From inside the lift I can see the laser beam come in one window but it doesn't go straight across the lift, it bends towards the lift floor and misses the opposite window. The laser beam appeared to bend because I were accelerating while it was crossing the lift. This is summed up in the animation to the right. (There's also some animated explanations here: http://www.drphysics.com/syllabus/equiv/equiv.html)

Now the principle of equivalence says that a accelerating lift is no different from a lift at rest on the Earth's surface. And since the laser beam bent in the accelerating lift, it should also bend if fired across a lift on the Earth's surface. Indeed light rays are bent by gravity, just as Einstein showed, although on Earth the deflection is only very slight. The deflection of light by the Sun's gravity was detected back in 1919 by measuring the position of stars behind the Sun during a total eclipse.

Abel 2218 Still don't believe that light can be bent by gravity? The image to the right shows this effect quite dramatically. It is a Hubble Space Telescope image of a cluster of galaxies. The total mass of the cluster of galaxies is so much that it bends light rays from distant background galaxies producing strange "arcs" in the image. The gravity of the cluster is acting like a giant lens, magnifying the distant galaxies in the background - this phenomenon is called gravitational lensing.

In terms of Einstein's geometrical theory of gravity (general relativity) the deflection of light is because light is moving through curved spacetime - it's really just following the distortion of space around the cluster of galaxies.


1.5 Redshift

There's one last bit relativity we have to deal with: redshifts and the Doppler effect. First let's deal with the Doppler effect.

You have probably noticed the Doppler effect with sound before. As an ambulance overtakes you at high speed the pitch of its siren seems to change. As it hurtles towards you the pitch seems higher and once it has past you and is moving away the pitch seems lower.

There's a similar effect with light (but it works for different reasons than it does with sound). An object moving towards you will look "bluer" than it did at rest, and an object moving away from you will appear "redder." The difference is only noticeable when considering very high speeds, close to the speed to light (which is about 6.7 billion mph!). When objects appear redder they are said to be redshifted, when they appear bluer they are blueshifted. This is another consequence of special relativity and has been put to use in many situations. For example, the radar "speed guns" that police use to measure the speed of passing cars make use of this effect. The change in frequency ("pitch") of a radio beam bouncing off a moving car can be used to deduce the speed of the car. It's the Doppler effect that causes the radar beam to change frequency and the amount of frequency shift is a measure of how fast the car is moving.

Movement is not the only thing that can cause a redshift, gravity can. Gravity not only alters the path of light it also affects its frequency (colour). Strong gravity produces a redshift - the gravitational redshift. One way of thinking about gravitational redshift is this. As the light escapes from the gravitational field of a massive object it looses energy, but it can't slow down - light (in a vacuum) always moves at the speed of light. So instead of slowing down it loses energy by becoming lower frequency (less energetic) light. Another explanation, more in terms of Einstein's theory, is given in Chapter 5


1.6 Black holes

Now we can get black to those black holes at last!

Let us consider what happens when we take a star of a certain mass, let's take the Sun this time, and make it smaller (crush it). The gravity on the surface will increase, because we're moving the surface closer to the centre. Einstein would say that the spacetime around the surface is getting more and more curved as we shrink the star. The amount of light bending and redshifting that happens close to the surface increases as the gravity (spacetime curvature) becomes stronger. When the Sun is crushed to only 6 km across the redshift from its surface is infinite - this is also the point where the escape velocity reaches the speed of light - no light can escape at all. If the Sun was to be crushed to only 3 km radius (6 km across) it would be a black hole.

The event horizon marks the "point of no return," and for the Sun this would be a sphere with a radius of 3 km. Outside of this it is always possible (albeit difficult) to escape the gravity. If you go through the horizon (i.e. closer than the 3 km perimeter) then there's simply no way out - gravity wins. There's no magic to black holes, only gravity. As long as you steer clear of the event horizon you will not get sucked in. As you move closer to the horizon the rapidly increasing gravity makes it harder and harder to escape (the escape velocity is higher the closer you get), so don't get too close!

black hole bending light What does this newly formed black hole look like? It really does look like a black hole in space: A circle 6 km across (a sphere really) that is pitch black. Trouble is, space is black, so you need some light behind the black hole before you would notice it. The stars of the night sky make a nice background; around the edges if the black hole are distorted and reddened images of the stars in the background. This is the light that's being lensed and redshifted as it passes close to the horizon.

The illustration to the left (by Robert Nemiroff) shows a star field (left) and the same field but with a black hole in the way (right).

As no light (or anything else) can get out of the black hole, they turn out to be remarkably simple objects. The one-way barrier of the event horizon means that no information (about what's inside) can get out. So it doesn't really matter what went into making the black hole, from the outside it makes no difference. Black holes all look pretty much alike.

A black hole has only three characteristics: mass, electric charge, and rotation rate. The size and shape of the event horizon is determined by these three characteristics, but it almost always close to spherical. Apart from that they are, from this point of view, amazingly simple. It doesn't matter what went into making the black hole, a solar mass of starstuff or a solar mass of old socks... the resultant black hole would be exactly the same. (Black holes don't smell!)


Maintained by Simon Vaughan (sav2 at star. le. ac. uk)
Last updated: 18/11/2003
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