Saturday, March 19, 2011

Research Paper on Black Holes

Research Paper on Black Holes

Black Holes. Fact or Fiction? Over the years black holes have been portrayed as portholes to other dimensions or times, gates across the galaxy, objects of death and destruction, or all of the above. Black holes are real, that is one of the few things that we do know about them for sure; we also believe that we have a firm grasp on how they are created and what they do, but their purpose still remains a mystery.

What is a Black Hole?
To answer that question right off: a black hole is an area in space that has so much gravity that nothing, not even light, can escape. That is the short answer; there are many different kinds of black holes and they all react differently (whether it’s how long it takes for you to die after you’ve been sucked in, or how it eats the closest star¾they all act differently). A good way to describe a black hole would be this: Let’s say you’re standing somewhere on Earth and you throw a baseball up into the air. It’ll go up for a while, but it will eventually come back down; Now let’s say you throw that same baseball up at twelve kilometers per second (11.2 is Earths escape velocity); that ball will continue up, passing through the Earth’s atmosphere and into space continuing at that speed forever and ever.

Now let’s say that you’re standing on an object with such a huge mass that the escape velocity is greater than the speed of light. Not only would you be flat, but you wouldn’t be able to throw that ball out of the Earth’s atmosphere. That is a black hole.


Different Kinds?
Yes, there are different kinds of black hole. Three that we know of to be exact. They are:
Static (Schwarzschild), Charged (Reissner-Nordsrom), Rotating (Kerr), and Supermassive. All four kinds are made up of the same basic elements. The Photon Sphere, the Event Horizon, and the Singularity. The Rotating black hole, however throws a new element into the mix. It has not one, but two Photon Spheres, and what is called an Ergosphere. I will cover all that in more detail a little later.

How big?
How big? Well to answer that we have to get a little bit more specific. Mass or space. We will talk about mass first.

A black hole can have as much or as little mass as it wants. It’s just a matter of how compressed it is. It is not a fact, but we believe that almost all black holes were made from the collapse of giant stars...that is to say that our star, The Sun, is probably not big enough to become a black hole. Since we think that it is the death of a giant star which creates a black hole, we also assume that the black hole has about as much mass as the star’s just a whole lot smaller. It is believed that the standard mass for a black hole is about 10 times the mass of the Sun (or 10^31 kilograms). That number would look something like this:

That’s how big a black holes mass should be if our calculations are correct.
It’s obvious that the bigger a black hole is the more space it takes up; the Schwarzschild Radius (the radius of the horizon) and the mass are exactly the same. That is to say that if one black hole is 50 times heavier than the other, it’s radius is 50 times larger. Simple, no?

Black Hole Energy
Theoretically you can get energy out of a black two different ways. You can set up a dumping station and dump things into the black hole. Or you could throw thing near it (this method would only work on rotating black holes).

But I’m getting ahead of myself. First off, let me give you the formula for getting energy from a black hole:
E-released = (mass)(speed of light)^2[1 - (1-Rs/radius)^1/2]
It looks complicated in a simple kind of way. It really means that the energy of anything is just the mass times the speed of light, squared (3x10^8). All that means is that there is a lot of energy in matter.
Getting right down to it, it has to do with gravitational energy (which I will explain in more detail latter). The closer an object gets to a black hole the more energy is released. Just how much energy depends entirely on the weather...or rather on Rs/radius. So to simplify it even more, the farther away an object is the amount of energy released wants to go towards 1%, and the closer it gets it moves towards 100%.

It’s math, something I don’t have a very good grasp on...but that’s not important. What’s important is that we know how it creates energy. All I’ve given you is math, now it’s time to go into details.

Theoretically we send a dumping station with rockets on it, a large conveyer-belt, and a whole lot of trash into space. We attach the conveyer-belt to the dump station and the electric motor (we can’t forget the electric motor). As the conveyer-belt turns, trash is dumped off into the black hole. Every time something is dumped the conveyer-belt jerks and turns a generator which produces a huge amount of electricity. Much more efficient then anything that we have today.

Space and Time
It is fact that you can pin-point a place in space with three coordinates. X Position, Y Position, and Z Position. Or, with those same three numbers, you could give something depth; we’ll say 5x7x9. That could be a room, it could be a box...or it could be just an empty space. Who knows?

Now that we’ve covered the basics we’re going to confuse you by adding another number into the formula. Time. So now we can say that it was right there at this point in time. So whatever happened with that thing that we were just talking about we know exactly where it was and when it was, this set of coordinates is known as space-time.

There was a guy who lived a while. Crazy guy, always coming up with theories, doing math. Just for mystery’s sake we will call him “Al”. Now Al came up with the crazy idea that gravity was not just an everyday force. He said that without it we would all be flat; that it actually curves space. So this guy, Al, says that the more dense the matter is the more space is curved around it. So what a black hole is doing sitting there in the darkness of space is curving it. But where does it curve to? What direction does it go? Well, you remember the added dimension? That fourth one that we added? Time? Yep, it curves space into time. Distorting both, theoretically. Oh, yeah, what was this guy’s, (Al’s) last name? Einstein, I think.

Things orbit around black holes just like we orbit around the Sun. Different things orbit around black holes rather than planets, though. However, they are slightly larger things like stars. There are two very different theories as to how things orbit around them; there are the Newtonian orbits and the Straight Line orbits. The Straight Line orbits come from Einstein's General Theory of Relativity and are almost the exact opposite of straight. The orbits curved and very chaotic, as seen the picture below. This form of motion is not completely accurate, but it is not fictional. We have measured a similar orbit by watching Mercury over the past several years.

The Newtonian orbit is just a standard orbit moving around an object on the same path as seen in this picture.

How long do they live?
Whereas radiation is a cause of death on this planet, radiation means existence to a black hole. No radiation, no black hole. It radiates particles and anti-particles, thus it is constantly loosing mass. Essentially, it is evaporating. The smaller the black hole gets, the less it has to hold it together, the faster it radiates, the quicker it dies. Theoretically, in a black hole’s last seconds it radiates more energy than one billion megaton hydrogen bombs would. After that it would simply fizzle out.

Falling In
There is a question that goes around every once in a while. What happens when you fall in? There are really four possibilities: You’ll die, you’ll get sucked into another dimension and die, you’ll travel through space and time (not necessarily both at once), or you’ll get sucked into another dimension and live.

Just for fun, let’s say you get into your space ship and head straight toward the Supermassive black hole at the center of the galaxy. After a while you turn off your rockets for a gentle coast in.

At first you feel just like you do when in space. Nothing’s really different. You and the space ship are traveling the same way at the same speed; you are weightless. You are now getting closer and closer to the black hole’s center. You begin to feel the tidal forces of gravity. If your feet are closer to the center than your head you will feel stretched (you’d feel stretched if your feet were further and your head was closer, so it really doesn’t matter what closest) because they are closer and are getting more of the gravity then your head. As you get closer to the center these forces get stronger and stronger and eventually you and your spaceship will be ripped to pieces.

The larger the black hole the longer it takes for the tidal forces to get to you. The one that you’re falling into is about one-million solar masses so you won’t even feel the tidal forces until you get to about 600,000 kilometers away from the center. The reason I said to jump into such a large hole is because we want you to live past the event horizon, for a little while anyway. If you jump into a black hole the size of the Sun the tidal forces would make you very uncomfortable at about 6,000 kilometers out, but that wouldn’t matter because you’d be ripped to pieces before you even crossed the event horizon.

After crossing the horizon, space-time becomes so warped that time (t) and radial distance (r) switch roles; r begins to describe how long it will take to hit the singularity and t will describe the distance you have left to go. In other words, once you’ve crossed the horizon the singularity is in your future. There is no escape.

I have a friend...
Really? That’s great! So do I! Oh...wait...ok, another question. I have a friend, her name is Penelope Toop (I guess that the last name doesn’t matter...). She is standing out side of the black hole watching me getting sucked in (and probably laughing about it). What does she see?

Well, before we get into this I will inform you that at one point in time black holes were called “frozen stars” and for a very good reason. What Penelope sees is this:

You going steadily toward the horizon, but never falling in. You’ll continue to get smaller and smaller as you get toward the horizon and then you’ll appear to stop, to freeze in place. The same is for the material that formed the black holes. Which is why they were once called frozen stars. A star collapses, but all that matter that created the black hole will continue to shrink until it just freezes, not quite reaching the Schwarzschild radius.

All this that she sees, however, is nothing more than an optical illusion. It doesn’t take an infinite amount of time for a black hole to form and it certainly doesn’t take an infinite amount of time for you to fall in and die. As you get closer to the horizon, the light takes longer to reach Penelope. Theoretically, right before you cross the horizon the light that hits you will stay there forever. Everything that has ever crossed the horizon should still be visible from the outside.

You could also look at this another way. Time may actually be slowing down, distorted by the immense gravitational fields. Let’s say you drop Penelope off at a safe distance and then fly toward the black hole. As you’re just about to cross the horizon you turn on your reverse thrusters to keep you from being pulled in. Eventually you break free and return to Penelope triumphant because you won the ten dollars that you bet. Once you get back to her you find that she has aged much quicker than you. Time had slowed down.

The real question is which one is true? The short answer: They both are. The answer truly depends on the coordinate system that you use. What people normally use is called “Schwarzschild Coordinates” you’ll cross the horizon when t (time) is infinite, so with these coordinates it really does take an infinite amount of time to cross, but the reason is that the Schwarzschild Coordinates distort everything around the horizon, infinitely distorted, or, to use the correct term, the singularity.

Any other coordinate system will tell that the time it takes to cross is indeed finite, but the light gets frozen so it seems infinite.

What do I see?
You really don’t see much of anything. Possibly images of long forgotten times and places, but these images will be distorted in strange ways because the black holes gravity bends light. You will also be able to see everything that is happening on the other side of the black hole as well, since the light can still easily reach you.
How long will it take you to reach the singularity? It depends on where you start from and the size of the black hole. Since we’re still in the one-million solar mass black hole we’ll say you start when the distance from the singularity is ten times the radius of the hole. It should take you about 8 minutes to reach the horizon and after that a whole seven seconds to hit the singularity. However, you must realize that time scales with the black hole; in a smaller one death would come much quicker.
Once you’ve crossed you may try to get out, but it is inevitable. The singularity is now in your future, so just sit back and enjoy the ride.

“Well,” you say, “if a black really does exist and it’s sucking up everything around it...wont it one day suck up the entire universe?” The answer is simply, no. This is because of the Event Horizon; everything that passes this point will be sucked in, but if it doesn’t pass the Horizon then there is no way it could suck it up. Kind of like a vacuum; it won’t suck anything up unless you put something in front of the nozzle.

Then you ask: “The Sun...could it...?” It is mathematically impossible for the Sun to become a black hole. If for no other reason then the fact that it’s not big enough to do so. It would have to weigh many times more than it does. What our sun will do when it dies is quickly grow into a Red Giant disintegrating Mercury and Venus and making life on Earth rather uncomfortable. Then it will recede to a white dwarf and spend the rest of its days small and insignificant. No danger there.

There is plenty of evidence to support black holes. Although you can’t see black hole’s directly since no light can escape from them, there is evidence to support their existence. Let us say that we have a region of space that we think might contain a black hole. How do we know? How can we find out? First of all, we must measure how much mass is in the area. If it’s a lot, concentrated in a small area, and if it’s dark then it’s a good bet that we have got a black hole. Right now we look for two kinds of systems that could say “a black hole is here”; things like the huge amount of mass and gravity positioned at the center of most galaxies, including our own Milky Way. Also we look for Binary Star Systems that have an unusual amount of X-Rays emanating from them.

To date, there are eight known galaxies that are thought to contain Supermassive black holes at their center. These Supermassive black holes range anywhere from one-million to one-billion times the mass of the Sun. We measure the mass of any black hole by the speed the stars and gas travel around the area we suspect contains a black hole. It’s simple; the faster the speed, the more gravity is required.

How Do We Find Them
Black holes have a large amount of materials orbiting around the outside of the hole. All of these materials come together to form a disc-like shape. These discs have twin jets that are perpendicular to them, and these jets cause a highly abnormal amount of X-Ray radiation to emanate from the black hole. So finding the black holes is very simple; most scientist simply use an X-Ray telescope and look for a large amount of X-Ray radiation in one area.

Astronomers use another method with the accretion disks called redshifting. The Doppler effect is a great example of what “redshifting” is, exactly. Take a car traveling at a high speed toward you honking it’s horn. From a distance, the horn seems to be at a higher pitch than usual. When it passes you the horn seems normal, and while it’s moving away from you the pitch seems to be lower. That is almost a perfect example of redshifting. Light, when it is moving away from you seems to have a lower frequency than light that is moving toward you or even passing by you. If you look at a yellow star that is moving away from you it may appear red, because the light is at a lower frequency. A black hole emanating X-Ray light moving away from you will get redshifted to the point where it almost becomes visible light. Blueshifting is just like redshifting only in reverse. If it is moving toward you instead of away from you it’s called “blueshifting“.

Lets Go Inside
We’ve talked about a lot of different things pertaining to black holes, but we have not yet gone into real detail about what exactly is inside of them. As I have said before, the black hole is made up of three main parts: the Photon Sphere, the Event Horizon, and the Singularity. Now we will discuss these things in greater detail as we go inside.

This is your normal, everyday, nothing out of the ordinary black hole, the static kind. It doesn’t move and it’s not charged nor is it Supermassive. In order, from outermost to innermost, it is made up of the Photon Sphere, the Event Horizon, and the Singularity. First we will talk of the Photon Sphere.

The Photon Sphere. It’s a very simple name for a very simple reason. First of all it’s a sphere; secondly photons are what make up the sphere. To be more specific, it is the only place in a black hole where light will have a very unstable balance. Just like when you’re orbiting a planet, the closer you are the faster you need to be going to keep from falling down. That is the closest light can get without being pulled in; amazingly it’s just not fast enough.

Although light is a very fast thing it’s not fast enough, as we have discovered. It’s orbit in the Photon Sphere is sadly temporary. Why? First of all, the photon sphere is a very small place, for the light to stay in orbit it would have to hit the photon sphere just right or else it would eventually either fall into the black hole or fly out into space. Even if it does hit the photon sphere and does orbit for thousands of years it will only be a matter of time before it hits another beam of light and is knocked into oblivion. It will happen, I can guarantee it.

Now onto the Event Horizon. The Event Horizon is just like the Photon Sphere. It is all in the math; a simple part of the Swarzschild radius that is telling us what is what and why it’s doing what it’s doing. But what is it doing? Well, the Event Horizon is the point from which nothing can escape the black hole. Once you cross it you are going to die; but look on the bright side, if you die in a black hole you will be a whole lot thinner.

I guess that I should add that all of this is theoretical. So let me put it this way: Theoretically you could fly your space craft to just a few inches away from the Event Horizon then fire all your rockets in a full reverse and if the escape velocity that was required wasn’t so great that it’d squash you, you could easily get away from the black hole.

Of course, you know by now that once you cross the Event Horizon time-space are switched. The singularity, and ultimately your death, are now in the close future. Completely inevitable. Kind of depressing, isn’t it?

Well, I’m not going to talk about the Photon Sphere this time. If you want to know what it is just turn back a page and you can read all about it there. I say this because even though we are talking about a Charged black hole instead of a Static black hole the Photon Sphere is no different. So onward we go to something interesting. The Event Horizons.

That’s right, I said Horizons, as in two of them. This black hole does not listen to reason. It completely blows Schwarzschild’s Radius out of the water. So someone else had to com in and talk about it. Their names were Reissner and Nordstrom.

You see, it’s like this. If you add a little bit of charge to the black hole the Event Horizon shrinks and creates a second horizon just outside of the singularity. The explanation to what goes on between these two horizons is this. Time just seems to stop. Scientists cannot explain why this happens, but it’s all theoretical anyway.
If a charged black hole continues to gather energy all it’s life the outer horizon will grow gradually smaller while the inner horizon will continue to grow bigger. If the black hole acquires so much energy that it equals it’s own mass (an insane magnitude of 10^30 coulombs) the two horizons will cancel each other out leaving a naked singularity.

A naked singularity is just the singularity without the horizon. For some reason after the black hole loses it’s horizons and becomes a naked singularity, it no longer has the same amount of pull on everything around it. Meaning that you could just walk right up to a black hole and then get away from without needing to travel many times faster than the speed of light.

Now on to the last of the different kinds of black holes, rotating. They are sometimes called Kerr black holes just like charged are sometimes called Reisner-Nordstrom. The difference is in how the geometry is used. You measure static and charged with a two-dimensional polar grid to figure out exactly what it’s doing. When you’re going to try and get the coordinates for a rotating black hole you must take that grid and wrap it around a sphere into what’s called an oblate spheroidal coordinate system.

So why do they call it a rotating black hole? You would assume that it’s because it rotates, but that is not technically correct. If they call it a rotating black hole simply because it rotates then almost every black hole would be called a rotating black hole. Most black holes rotate at speed that is about 99.8% of their mass. Well, we’ve now established how a rotating black hole is the same as others, let’s move on to more interesting matters and explain why they are different.

The Photon Spheres. Good things come in twos...I guess. In this case the rotating black hole has two Photon Spheres, as I have already said, and also two Event Horizons, but I’ll explain more on that a little later. The two Photon Spheres have to do with why exactly it’s called a rotating black hole. You see the Photon Spheres both rotate, and while they rotate they drag space with them creating a kind of whirlpool in space.

We’ve got the fact that there are two of them, but how do we know that they actually work? Well, the short answer is that we really don’t. Theoretically, it works like this:

Let’s say that you have two satellites orbiting the Earth. One is closer in to the Earth than the other. The one that is closest to the Earth must have a greater speed than the one that is farther away or else it will not be able to sustain an orbit and will crash into the planet. No, not so in terms of the black hole. As we have already talked about, the Photon Sphere carries light in an orbit around the black hole. So, in order for there to be two Photon Spheres light must travel around the black hole in two different places. “But how is that possible?” you ask, baffled, “light travels at a constant rate, it doesn’t slow down or speed up!” That is true, and scientists have no real explanation for why it does what it does. Perhaps it is simply that space-time is so distorted around the black hole that light will kind of speed up, or kind of slow down. Who knows?

Now we come to something entirely new. The Ergosphere. It is neither a part of the Photon Sphere nor apart of the Event Horizon. It is a completely unique part of a rotating black hole. The Ergosphere is not really a sphere at all, but an ellipse, a 3D ellipse to be exact. It is very visible and not just a radius like the Event Horizon and the Photon Spheres. It is made up of anything that gets into the black hole. In this case the black hole is spinning so fast that it literally blows some of the particles from what it has sucked in, out. The faster the black hole rotates the bigger the Ergosphere gets. It is also a very strange phenomena because of the fact that it is positioned directly between the two event horizons, but neither the first, nor the second, Event Horizon is the point of no return.

On the very outside of the Ergosphere is what is known as the static limit. This means that once you cross that point you can no longer remain static, you will begin to move towards the singularity as if you had crossed the Event Horizon.
There is no need to talk about the Event Horizons for this black hole. If you must know what it is like, than turn back to the charged black holes and read about them there. It’s just the same.

Ok, this is going to be short and sweet. A Supermassive black hole is just a really big black hole. Theoretically, it can be any of the following: Static, Charged, or Rotating. The only real difference is that they exist within the only place that they will fit. Namely the center of galaxies like our own Milky Way. Some scientists even believe that the reason the galaxies rotate is because they contain a Supermassive black hole at their centers.

The End?
Not really, not anywhere close actually. Black holes, science-fiction, or science-fact., will always be a curiosity. People will look to the stars, or to the centers of galaxies and ask what is their purpose? Do they lead anywhere? If so, where? Can the energy that is within them ever be harnessed for our use as an unlimited energy supply? Will we ever be smart enough to get close enough but not fall in? Well, you get the holes are out there; and we will continue to study them. They will always be stars.

Warning!!! All free online research papers, research paper samples and example research papers on Black Holes topics are plagiarized and cannot be fully used in your high school, college or university education.

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