What are Black Holes?

An object sits in space minding its own business. A rocket is fired from its surface. What happens?

To escape from the surface of the object, the rocket must overcome the pull of gravity.

The faster the rocket is propelled upward, the higher up it will travel before it falls back to the object. There is a critical speed beyond which the rocket will just escape the gravitational pull of the object and escape to freedom.

This critical speed is known as the

escape speed = [2GM/R]^1/2

(which is a measure of how strong gravity is at the surface of the object). Some examples of escape speeds:

OBJECT	Escape Speed (km/s)
Moon	2 km/s
Earth	11.2 km/s
Jupiter	60 km/s
Sun	620 km/s
White Dwarf	6,900 km/s
Neutron Star	200,000 km/s
Black Hole	c

A black hole is an object from which the escape speed is equal to c, the speed of light. Consequently, light cannot escape from the object (and the object appears black!)

Because the speed of light is the maximum speed at which anything can travel through the Universe, this also means that nothing can travel fast enough to escape from a black hole.

i

Event Horizon

Question: What is the surface of a black hole?

According to Newton and Einstein, the strength of gravity around an object doesn't depend upon how the material is arranged inside of the object as long as the distribution is spherically symmetric. This means that the mass of the star could, for example, either be spread evenly thoughout the star's interior or concentrated at the very center of the star; we wouldn'be able to tell from the outside.

Question: How is the material distributed in a black hole?

It turns out that all of the mass of a black hole resides at its very center (in a mathematical point); this point is referred to as a singularity. Note that a mathematical point has no length, height, or width and thus has zero volume. So, if I cram all the mass of the star into the singularity ===> the density of material at the singularity is infinite. (This can lead to interesting effects.) Anyway, back to the surface of the black hole. So what is meant by surface of a black hole? Because all of the mass is contained in the singularity, we define the surface of the black hole to be the radius from which the escape speed is equal to the speed of light, c (recall the expression for the escape speed). This surface is a natural boundary; it separates our Universe into two parts:

• an inside part cut-off from the outside world in the sense that an observer in the inside can only receive information from the outside world; there is no way for an observer on the inside to send a message to someone on the outside.

• an observer on the outside can only send information to an observer on the inside; the outside observer cannot hope to get a response in return.

The imaginary surface that separates the Universe into these regions is called the Event Horizon.

The radius of the event horizon of a non-rotating black hole is

R_s = 3 x [M/M_Sun)] km .

R_s is referred to as the Schwarzschild Radius in honor of Karl Schwarzschild, the first person to work out the theory of a non-rotating black hole.

The Sun would have to shrink to a radius of 3 km in order to become a black hole. A 10 M_Sun black hole would have a radius of 3 x [10M_Sun/M_Sun] km = 3 x [10] km = 30 km.

Question: What kinds of things can happen near the Event Horizon?

If a clock is dropped from infinity toward a black hole, the observer who dropped the clock would see:
• that when the clock is far from the black hole and its gravitational pull is weak, nothing funny happens at all. The clock behaves as Newton would have predicted. (Note, however, that the motion is not exactly as Newton would have predicted; there are effects due to Einstein's general theory of relativity, they are just weak.)

• It is only when the clock nears the event horizon where gravity becomes strong (because F = -GMm/r²) that strange effects start to occur.

• The clock run more slowly as it falls into the strong gravitational field of the black hole; at the event horizon, time appears to freeze according to the observer sitting at infinity. The clock would never appear to cross the event horizon according to the observer sitting at infinity.

• The light emitted from clock would be redshifted as it moves into the gravitational field of the black hole. The observer who dropped the clock observes more and more strongly redshifted emission from the clock as it approaches the event horizon. At the event horizon, the light is redshifted to infinite wavelength (zero energy).

• The clock would get stretched by Tidal Forces as it approaches the event horizon.

  The Moon raises two tidal bulges on the Earth because of tidal forces. (The Earth also raises tidal bulges on the Moon.)

  The Tidal Forces may even tear the clock apart before it reaches the event horizon.

Interestingly, if an astronaut tagged along with the clock on its journey, the astronaut would not feel anything unusual about the trip (other than the strong tidal forces). The astronaut simply falls toward the black hole, pass through the event horizon, and then flow into the singularity. The astronaut, however, sees interesting things. The black hole acts like a lens leading to several effects.

Some Properties of Black Holes

• Cosmic Censorship
  Nature always cloaks singularities with event horizons. So, no matter what strange physics may occur near singularities, it cannot reach back into our Universe.

• Black Holes Have No Hair
  Black Holes are characterized by only their mass, spin, and electrical charge. This is odd, as it says that it doesn't matter if we make black holes out of elephants or gnats or old socks, it is only the mass, charge, and spin that are important. If I throw neutral material into a black hole, I do not know if I threw in electron-positron pairs, proton-anti-proton pairs, neutrons, neutrinos, ... . That is, we lose information about our Universe as it passes into a black hole. [Comment--if this information manages to sneak out into some other universe through some quirk, then the other universe would notice things that occurred randomly and without warning (the notion of cause and effect breaks down). This is bad.]