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A black hole is theorized to be a collection of collapsed matter of whose gravitational pull is so strong that not even light can escape its force. The matter is is forced in a very, very tiny area and therefore the matter is very dense. Since light cannot escape, they are considered to be truly black. This, obviously, makes it hard to detect an actual black hole, and therefore, have only been theorizd to exist. These theories are slowly turning into "conclusive evidence." This evidence includes the particle dust given off from matter entering the black hole, as well as observations of orbits of bodies near the black hole.
Black holes are usually formed after supernova explosions, in which the remnants of this explosion implodes within itself. It will continue to condense to a volume of zero and infinite density. This is known as a singularity.
How do we know?
Karl Swarzschild first came up with the concept of black holes in 1916. This was based upon Einstein's theory of relativity. The Swarzschild radius is the radius where the escape velocity equals the speed of light. The Swarzschild radius can be calculated using the escape velocity equation:
vesc = (2GM/R)^1/2
Substituting the speed of light for the v:
R = 2GM/c^2
If you notice, the Swarzschild radius is only dependent upon the mass of the body. Anything that enters this radius will not exit, due to the tremendous amount of gravitational pull.
So, How do we know?
Again, as mentioned earlier, we can't directly observe a black hole. We can, however, make observations to the surroundings around the black hole. It used to be that theorists were the only scientific persons who acknowledged an existence of black holes, however, today, the story is quite different. The popular idea today is that black holes do exist and are common in all the galaxies so far investigated. One reason is Einstein's theory of General Relativity. This theory accounts for the existence of black holes, and if they do not exist, then the General Relativity theories by Einstein would be wrong. Considering all the tests and experiements done to date to try and disprove this theory have all been rejected, this seems unlikely. Also, scientists today look for high concentration of mass in a small area. Calculations and technology allow this to happen. Another factor in proving the existence of black holes is the Hubble Space Telescope. The Hubble Space Telescope has accumulated a large amount of data and information supporting the existence of black holes.
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Dick and Jane
Suppose there were Dick and Jane. Now they're going for their daily intergalactic space ride in their seperate Super-Speed Rocket Cruisers when Dick suddenly loses control of his Cruiser and ends up crossing into the Swarzschild radius of a black hole. Jane, with good intuition, knows there is nothing she can do. So, what does she see?
Jane will never actually see Dick reach the "event horizon," or the boundary at which light can enter but never escape. Dick will surely reach the event horizon, but not from Jane's perspective. As Dick becomes closer and closer to the horizon, the light emitted from Dick will take longer and longer to reach Jane. As Dick reaches the horizon, the light will not be able to escape, and therefore never reach Jane. Dick will appear to be "frozen," or standing still to Jane.
Dick loses control of his Rocket Cruiser, but this time ends right on the brink of the horizon. He hasn't crossed the horizon, but is as close as you can get. He returns to Jane to find her much older, and yet hardly any time has passed to Dick. What's going on here?
This is a strange concept. Time has passed more slowly for Dick when compared to Jane.
It turns out these two situations involve the same concept. Using the "Swarzschild Coordinates," Dick will cross the horizon when the time is equal to infinity. But these coordinates offer a highly distorted view at or near the horizon. These distortions are mainly infinitely off. This is known as a singularity, where the laws of physics no longer apply. However, if you choose a different set of coordinates that are not singular, Dick will surely reach the horizon in a measurable time. But Jane will see Dick crossing the horizon in infinite time, since the light takes an infinite amount of time to reach her.
What's the Signifigance?
What's with all this black hole hoohaa anyways? Nothing about black holes is certain or set in stone. There are theories about black holes being connected with white holes. These white holes are supposed to be the opposite of black holes, in which matter is spit out instead of sucked in. This combination of a white hole and a black hole is called a wormhole. Theories are that a wormhole may be connected to a completely different universe. Theories have been brought up that this may offer the possibilty of fast and convenient space travel. Possibilites of time travel have also been brought up from these worm holes. Traveling back to the past is a widely considered possibilty. However, as cool as these are, these are just theories and nothing is certain. Actually traveling through one of these can't be all that comfortable anyways. But hey, we can dream.
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