What are Black Holes?

Suppose we have an object of mass M and radius R, i.e.,

For a rocket to escape from the surface of the object, it must overcome the pull of gravity.

It is clear that the faster the rocket is propelled the higher up it will travel before it falls back to the planet. There is a critical speed at which the rocket will just escape the gravitational pull of the planet and escape to infinity.

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.

A black hole is an object whose escape speed is equal to c, the speed of light ===> light cannot escape from the object (and the object appears black!)

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

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 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 most of the mass could be concentrated at the very center of the star, we simply wouldn'be able to tell from the outside. Hmmmm, what does this notion imply about black holes?

Well, it turns out that all of the mass of a black hole resides at its very center (in a mathematical point); this thing 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 infinitely large. This leads to some interesting problems (e.g., across this surface, the separate notions of space and time, in a limited sense, reverse). Anyway, back to the surface of the black hole. Because all of the mass is contained in the singularity, we define the surface of the black hole to be given by the radius from which the escape speed is equal to the spped of light, c. This surface is a natural boundary which separates the Universe into two parts:

• an inside which is cut-off from the outside world in the sense that an observer in the insider can only receive information from the outside world; there is no way for the observer inside of the surface to communicate with someone on the outside.

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

This imaginary surface which separates the Universe into these regions is called the Event Horizon.

The radius of the event horizon is R = 2GM/c² and is referred to as the Schwarzschild Radius in honor of Karl Schwarzschild, the first person to work out the theory. The Scwarzschild radius is a small number, for a black hole the mass of the Sun,

Schwarzschild radius = 3 [M/M(Sun)] kilometers!

That is, the Sun would have to shrink to a diameter of 6 kilometers in order to become a black hole. Comment -- A 10 M(Sun) black hole has a radius = 3 [10M(Sun)/M(Sun)] kilometers = 3 [10] kilometers = 30 kilometers.

Further Comments

Some Properties of black holes

• Photon Trajectories
• Cosmic Censorship "Theorem"
  Nature always cloaks singularities inside of event horizons. So, whatever strange physics occurs near singularities cannot reach out 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 which 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. [Commet--if this information manages to sneak out into some other Universe through some quirk, then the other Universe would notice things which occurred randomly and without warning (the notion of cause and effect would break down). This is extremely bad.]