Introduction to Astrophysics/Black holes

A Black Hole is a theoretical object in physics in which gravity's pull is so strong that nothing can escape. The idea of a black hole comes from the idea that there is a universal speed limit, the speed of light. This creates an anomaly which we call an event horizon.

Event Horizon and the Schwarzschild Radius
The event horizon is essentially the skin of a black hole. It is the barrier between the inside and the outside of a black hole. When you are outside the black hole you are outside of the event horizon. You still have the ability to communicate with the rest of the universe, although your communications might be severely redshifted due to gravitational effects. Anything that crosses the event horizon may never escape. So you may be asking yourself right now how this event horizon arises and how do we determine where it is? The answer is, we calculate its Schwarzchild Radius. The Schwarzchild Radius was discovered in 1916 by Karl Schwarzchild. This was based off of the idea of a univeral speed limit and energy conservation. So lets do a non-relativistic derivation.

First we start with an equation of the total energy of a system.

$$E = \frac{1}{2}m_{1} v^2 - G \frac{m_1 M_2}{r}$$

Where $$m_1$$ is the mass of some arbitrary object, v is its velocity, G is the gravitational constant. $$M_2$$ is the mass of the massive object which will be our black hole, and r is the radius from the center of our black hole object. So we will now maximize the kinetic energy of $$m_1$$ by setting its speed equal to the speed of light. So:

$$E = \frac{1}{2}m_{1} c^2 - G \frac{m_1 M_2}{r}$$

As long as the objects total energy is positive it can escape from the black hole and not get caught in its event horizon. So what we can say is that if the energy of an object is less than or equal to zero then it is caught with in the event horizion. In other words:

$$ E \leq 0 $$

Which gives:

$$ \frac{1}{2}m_{1} c^2 - G \frac{m_1 M_2}{r_s} \leq 0 $$

Now solve for r:

$$ \frac{1}{2}m_{1} c^2 \leq G \frac{m_1 M_2}{r_s} $$

The $$ m_1$$'s cancel.

$$ \frac{1}{2} c^2 \leq G \frac{M_2}{r_s} $$

$$ r_s \leq G \frac{2 M_2}{c^2} $$

So as long as the radius is less than the value on the right then you are with in the limits of the black hole.

Cosmology and Black Holes
One question that physicists like to ask about astronomical discoveries is, what do these discoveries tell us about the nature of the universe? In specific, cosmologist want to know whether the universe is open or closed and growing or shrinking. Well the Schwarzchild radius has a little bit of something to say about this. Keep in mind that although this result is interesting it is not a final answer. It turns out that with some estimates of the mass of the universe and assuming a uniform density throughout the universe and the radius of the universe as determined by the Hubble constant, the universe may meet the Schwarzchild Radius requirements and have the critical density for being a black hole. But as any cosmologist will tell you the data's uncertainty is too large for scientists to decide one way or another what the true answer is. Black holes are one of the most important thing in the entire history of the universe because they have shaped the universe in the way it is.

Detection of Black Holes
The main problem with black holes is that they cannot be detected directly. We cannot see them. As a result Astronomers and Astrophysicists look for their effects. There are a few things that can be looked for.

First is an object orbiting around nothing very rapidly, as can be determined from relativistic calculations of centripetal forces. These can also be used to give estimates of the size and mass of a black hole.

The second thing scientists look for is accretion disks. These are disks of matter formed when the black hole is sucking mass and particles off of a near by object. The particles gain so much energy and heat that they begin to heat and radiate light. This can then be used to determine numerous things about the entire system. Often times the accretion disk is formed by the orbiting stars.

The third, and probably the less prevalent method involves measuring periodic X-Ray emmisions.

Theoretical problems with Black Holes
As popular belief may attest to, it turns out that black holes actually do present some theoretical problems for physics. One of the most major of all problems is energy borrowing. In physics, for some reactions to happen, some energy must be "borrowed" from the universe to create a specific particle. This will generally create 2 particles, the needed particle and its paired partner particle. For example a tau particle and a tau neutrino. Now say that this occurs right at the edge of the event horizon of a black hole and one particle gets sucked in while the other does not. The particles cannot recombine and annihilate back into energy. Now say that this happens indefinitely. What we can get is an infinite energy leak in the universe and an infinite mass increase within the black hole. This is a problem which must be explained by physicists.

Recent Discoveries about Black Holes
Here some recent discoveries will be mentioned but not explained.

Black Holes may not have smooth surfaces

There may be microscopic black holes all over the place.

Myths About Black Holes
During numerous particle accelerator openings there have been numerous protests, because protesters are afraid that using the particle accelerator will create massive black holes that will swallow the world. These people believe this due to the amount of energy created during these events. Contrary to their belief this will not happen. You must have incredibly massive objects confined to a very small space to create a black hole. Infact to turn the Earth into a black hole you would have to shrink its radius to about 20 mm.