History of the Theory of Black Holes
Black holes were first suggested in the 18th century by scientist, John Mitchell. He didn't think that they would be singularities (0 dimensional objects), but that they would be super-dense stars. The first person to predict a black hole as we understand them today was Karl Schwarzchild. He predicted them as a solution to the Einstein field equations (previously unsolved equations). Schwarzchild predicted that an object, if it were crushed down to a tiny size would have an escape velocity (the velocity at which an object would have to be moving to escape its gravitational pull) above the speed of light. This meant that nothing could escape a black hole because nothing can travel faster than the speed of light.
Event Horizons
The maximum radius of a black hole is given by the equation:
r = 2GM/c^2
where:
r is the radius of the black hole in meters,
G is the gravitational constant (about 6.67x10^-11 (m^3) / kg x s^2),
M is the mass of the object in kilograms, and
c is the speed of light (300,000,000 m/s).
The radius that this equation predicted is called the Schwartzchild radius, or event horizon. Inward of this point, nothing can escape the black hole.
A video of what it would be like to fall into a black hole: https://www.youtube.com/watch?v=QDlBXO19hwQ
Formation of Black Holes
Black holes normally now form from the collapse of very large stars (stars above about 1.5 - 3 solar masses, where 1 solar mass is the mass of our sun). Collapse happens when the star stops burning. This causes the star to collapse because the energy released by fusion is what kept the star from imploding. Without that energy, the gravity of the star pressing inwards is enough to compress the core of the star below its Schwartzchild radius, overcoming even neutron repulsion. Once the core has been compressed this far, it will last as a black hole almost forever. (Primordial black holes probably formed from unequal distribution of mass soon after the Big Bang.)
Formation of a black hole: https://www.youtube.com/watch?v=nqChdY5OyXY
Singularities
At the center of a black hole is the object that contains most of the mass of the black hole, the singularity. A singularity is a 0 dimensional object, an object that occupies no space. So a singularity is infinitely dense. A singularity forms because as a black hole forms, the pressure from gravity on the surface increases given that gravity is inversely proportional to the distance from the center. This means that as the star collapses, gravity forces it to collapse more and more and more, until it is a singularity. That is for non-rotating black holes. Rotating black holes have something even more confusing at their center, something called a ring singularity. A ring singularity is something that has no thickness, but that does have a radius. (All known black holes are rotating because the stars that formed them rotated. Non-rotating black holes are theoretically possible though.)
Accretion Disks
Once a black hole is formed it starts sucking in everything around it, forming an accretion disk, a disk-shaped area outside the event horizon full of matter being sucked towards the center of the black hole. An accretion disk forms in part because as the black hole rotates, it drags space-time with it. This is called "frame dragging". Matter that is pulled towards the black hole is forced to rotate with it by this process. It also forms because as things fall in towards a massive body, they spiral. Given that this gets all the matter rotating in the same direction, a disk is formed. This happens because as a particle orbits the black hole, it is constantly trying to fly away, which it starts to do. As it does this, it is pulled "down" (towards the plane through the equator) by gravity. By the time that the particle has been pulled all the way down, it is in the plane of the accretion disk.
Polar Jets
Many black holes also have polar jets, jets of super-fast moving protons and electrons that interact with each other and create high energy photons such as gamma rays. Astronomers are not exactly sure why these jets form, but the general idea is that as the matter on the accretion disk accelerates as it approaches the black hole, some of it gets shot out at very high energies in the polar jets. These jets can sometimes be as long as 5000 light years or 47,300,000,000,000,000 km.
Polar jets in quasars: http://www.youtube.com/watch?v=fo2F0UjcWNk
Spacetime
Spacetime is the 4D fabric that is the combination of the regular 3 spatial dimensions and time. Einstein's theory of relativity says that time is variable depending on your motion. Therefore, time is not always constant, and so must be considered as a dimension along with the conventional three.
A video of space-time and gravity: http://www.youtube.com/watch?v=jfv2AiVfnWA&noredirect=1
Warping of space time by a non rotating black hole.
We are pretty sure that there is a black hole at the canter of the Milky Way galaxy because the orbits of stars around the center suggest that there is something at the center with a mass of about 4.2 million solar masses. This massive object is quite small, with a maximum diameter of much less than 7,000,000,000 km (for comparison the sun is 1,391,000 km in diameter). With such a massive object in such a small space for such a mass, it is almost certainly a black hole.
This is a an artists rendition of Saggitarius A*, the black hole at the center of the Milky Way. The two circles of light spiraling in are super-massive stars. The blurring effect around the black hole is gravitational lensing, the bending of light by the extreme gravity around the black hole. In fact, the gravity around black holes is so strong that when looking at the event horizon, you see the entire thing, not just half of it as you normally would. The black part (the event horizon) is 12,000,000 km in diameter.
Types of Black Holes
All black holes are pretty similar. The only differences from one black hole to another are the mass, angular momentum, and electric charge. This means that the only things that the black hole saves from the matter that goes into it are the matter's mass, momentum, and charge. This puzzled scientists because according to quantum physics, information should not be able to be lost. It was later determined that Hawking radiation does preserve information.
Interesting intro to black holes (1 hr long): http://www.youtube.com/watch?v=9WbrujNXSw8
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