Black Holes

Black Holes

Imagine that you stand on the surface of the Earth and throw a rock straight up into the air. The rock will not sail into orbit and become a satellite, but rather will fall back on your head (ouch!). If you mount a rocket engine under your rock, however, you can push it far out into space. It could not only become a satellite, but might escape the Earth's gravitational pull completely. To do this, your rock has to go very fast – more than 11 kilometers per second. This velocity is called the escape velocity, the speed an object must achieve in order to overcome the gravitational attraction of a celestial body (be it a planet, a star, or a galaxy) and escape into space.
Objects with different masses have different escape velocities. For an object with mass M and radius R,

where G is a constant related to gravity.
It makes sense that escape velocity increases as an object's mass gets larger. (It takes more energy to escape from a more massive object and its stronger gravitational attraction.) The escape velocity is also higher for objects which are smaller. If you are trapped on the surface, then the smaller the object is the closer you are to all of that mass (and the harder it is to pull away from it).
- The Earth has an escape velocity of 11 kilometers per second.
- The Sun has an escape velocity of 618 kilometers per second, 56 times larger than that of the Earth.
- For a dense neutron star, the escape velocity is enormous – 60% of the speed of light!
- What happens when the object becomes more dense than a neutron star, and the escape velocity approaches or exceeds the speed of light?
Suppose that a neutron star core (the matter that remains after the star has thrown off great shells of gas in the form of planetary nebula) had a mass equal to 1.4 solar masses and a radius of 4 kilometers rather than 10 kilometers (its actual radius). The escape speed of such a neutron star would then be equal to the speed of light! This means that even light would not be able to escape the gravitational pull of this object. We call such an object a black hole (the name was invented by an astronomer who did not believe in black holes, just to make fun of the idea).
Black holes are expected have very strange properties. Nothing inside the black hole, not even light, can get out. That means that no pressure can hold such an object from collapsing in upon itself – in order for atoms in a black hole to withstand the pressure, they would have to move faster than the speed of light. Anything inside a black hole will thus fall to its center, compressed to infinite density and zero size. We call such a place a singularity, because the normal laws of physics break down.
Because nothing can stand still inside a black hole, the black hole is technically empty (it is a hole, after all!). Everything that falls into it goes straight into the singularity. The surface that surrounds the black hole is called an event horizon. Imagine if you were to fall into a black hole ... as you cross the event horizon you will notice nothing, but once you cross it there is no way back. You won't die by falling into the singularity, though, because long before you arrive the strong tidal forces will have torn your body apart (yikes!).
Einstein's 1915 theory of General Relativity predicts a stunning effect: strong gravity makes time run slower! Time on Earth is slowed down, compared to time measured by an observer in outer space where the effect of Earth's gravity is not as strong. For Earth's gravity, the effect is very weak: when we put an atomic clock in space and compare it with one on Earth, the Earth clock seems to be running slow by about 2 parts in a billion compared to the one in space. But atomic clocks are now so accurate that we can measure this difference and see that it is exactly what Einstein's theory predicts. There are two atomic clock standards in this country: one is located in Washington DC, and another one in Boulder, Colorado. Because Boulder is about one mile above sea level, the gravity there is a tiny bit weaker and the atomic clock runs slightly faster than the Washington clock. The difference is very small: the Boulder clock will run ahead by 1 second in 160,000 years! However, modern atomic clocks are so accurate that this difference is noticeable, and scientists must take it into account to keep the USA standard time properly!
The greater the gravitational force, the more time slows down. This time dilation causes the frequencies of photons emitted by atoms on the surface of a white dwarf to be reduced by about 1 part in 1000. We observe this as a gravitational redshift of the spectral lines. The gravitational redshift on the surface of a neutron star is much greater – 40%. But at the event horizon of a black hole, the gravitational redshift is 100% – any photon, be it visible light, a gamma-ray, or radio, gets redshifted to zero frequency, and thus becomes undetectable.
For someone outside a black hole, time appears to stop at the event horizon. Imagine that you fall into a black hole, and your friend orbits above you in a spaceship. You will quickly fall into the singularity, but your friend will see a very different picture ... for her, you never cross the event horizon but appear to hover just above it for the rest of eternity! In a sense this is just an illusion, as your image – the light that reflects off your body right before you fall through the event horizon – will take an infinite amount of time to get from the horizon out to your friend in the spaceship. This is a consequence of the fact that the light has to fight against the incredibly strong gravity of the black hole.