Black Holes

Hi, I Am Shirish Mishra, This is a Paper presentation on black holes created by me & my 4 friends Nakul,Prateek,Saransh & Aditya For Our College.The Research was done by nakul & the typing was done by me while all of us presented the paper in our class, 'Illuminati' was the name of our group....

Find Useful Resources On My Website : http://shirish.50webs.com/




Illuminati

Paper Presentation

B.Tech I Sem.

Information Technology

NIT

13 Oct. 2007



Black Holes


One of the horrors of a science fiction is falling into a Black Hole. In

Fact, black holes have now become really matters of science fact rather than science

Fiction. There are good reasons for predicting that black holes should exist, and the

Observational evidence points strongly to presence of number of black holes in our

Own galaxy and more in other galaxies.

In very general, a black hole is a region of

Space that has so much mass concentrated in it that there is no way for a nearby

Object to escape its gravitational pull. This pull is so strong that even light cannot

Escape this pull. But, let us first understand what this pull is. Law of gravitation

Suggest that every object exerts a force on every other object in universe. This force

is our pull in this case.

Suppose that you are standing on the surface of a planet. You

throw a rock straight up into the air. Assuming you don’t throw it too hard, it will rise

For a while, but eventually the acceleration due to gravity will make it start to fall

Down again. Now suppose you throw the rock hard enough, you can make

It escape the planet’s gravity entirely. It would keep on rising forever. The speed with

Which you need to throw the rock in order that it just escapes planet’s gravity (or
Planet’s gravitational pull) is called “Escape Velocity“. The Escape velocity depends on

mass of planet; if the planet is extremely massive, then its gravity (or its gravitational pull)

is very strong, and the escape velocity needed is also very high. The escape velocity also

depends on how far you are from planet’s centre (or centre of gravitational pull). The closer

you are, the higher the escape velocity needed to leave the area of gravitational influence of

the planet (or object).

Now imagine an object with such

an enormous concentration of mass in such a small radius that its escape velocity is

greater than the velocity of light. Then since nothing can go faster than light, nothing

can escape the object’s gravitational pull. Now, there are two theories about light :

One, which Newton favoured was that light is composed of particles

And the other that said light is made of waves. Under theory that light is made up

of waves, it is unclear that now it will respond to gravity but if light is composed of

particles, one might expect them to be affected by gravity in same way other objects

as rockets, cannonballs, and planets are. And the discovery that the light travels at a

finite speed means that gravity might have an important effect. Based on this assumpt-

ion, in 1783, scientist named Jon Michelle wrote a paper in Philosophical Transaction

of the Royal Society of London, in which he pointed out that :

“A star that was sufficiently massive & compact would have such a strong

gravitational field that the light could not escape: any light emitted would be dragged back

by the star’s gravitational attraction before it could get very far” (Stephen Hawking, 1998,
86).

Loosely speaking, a black hole is a region of space in which gravitational field is

so powerful that nothing can escape from it, having fallen past the event horizon. In

general, event horizon is a boundary for an area surrounding black hole, beyond which

events inside black hole cannot affect the outside observer(or outside world). But this

horizon has some really strange properties. To an observer sitting somewhere far away

from the black hole , the horizon seems to be a nice , static , unmoving spherical surface

but once you get close to the horizon , you realize that it has a very very large velocity. In

fact , it is moving outward at the speed of light! This explains why it is easy to cross

horizon in inward direction , but impossible to get back out. Since the horizon is

moving out at the speed of light, in order to escape back across it, one would have to

travel faster than light. One cannot go faster than light and hence you cannot escape

from black hole. “Trying to avoid centre of black hole once you’ve crossed the horizon

is just like trying to avoid next Thursday,” (Ted Bunn, 1955 , Q-1)

After having understood what a black hole is, let us now try to understand how a

black hole is formed. To understand this, we first need basic understanding of life

cycle of a star. A star is formed when large amount of gas, mostly hydrogen starts to

collapse in on itself due to it’s gravitational attraction, in space. As the gas contracts,

the atoms if the gas collide with each other more & more, heating up the gas. Ultimately,

the gas will be so hot that when the hydrogen atoms collide, they coalesce to form helium.

The heat released in this reaction makes the star shine. This extra heat increases pressure of

gas. This pressure goes on increasing until it is sufficient to balance the gravitational

attraction between atoms (or molecules) of gas, and as a result of which gas stops

contracting. Star(s) will remain stable for long time, with heat from fusion reaction

balancing the gravitational attraction. This could be better understood with the analogy,

“ It is bit like a balloon - there is a balance between the pressure of

the air inside , which is trying to make the balloon expand , and the tension in the

rubber, which is trying to make the balloon smaller.” (Stephen Hawking, 1998, 87)

However, sooner or later the star will run out of its

hydrogen & other nuclear fuels. So when a star will run out of fuel, it will start to

cool off and so to contract. But, in early 1920s , an Indian graduate student ,

Subrahmanyam Chandrashekhar , worked out how a star could still support itself

against its own gravity even after it has used up all its fuel. He suggested, when the

star becomes small , the matter particles comes very close to each other, and so by

according to Pauli’s Exclusion Principle, they must have very different velocities.

This makes them move away from each other and so tends to make the star expand.

Thus, a star can maintain itself at a constant radius due to balance between attraction

of gravity and the repulsion that arises from exclusion principle, same way earlier

gravity and heat were balanced.

But there is a limit to the repulsion that the exclusion

principle can provide . Theory of relativity limits the maximum difference in

velocities of matter particles in the star to the speed of light. Which means that, when

star got sufficiently dense , repulsion caused by exclusion principle would be less than

attraction of gravity. A cold star more than about one & half times the mass of sun

would not be able to support ( or balance) itself against its own gravity. But if it is less

than twice the mass, it will eventually stop contracting and will settle down to a stable

state. These state could be any of either a White Dwarf or a Neutron Star.

A star with a mass more than about twice that of the sun cannot

settle down as a White Dwarf or Neutron Star. In Some cases, the star may explode &

then throw enough matter to bring it’s mass below the limit. But this won’t happen in

all cases. In this case,

“Some stars will become so small that their gravitational field

will bend light to the point that it comes back towards the star. No further light, or

anything else, will be able to escape. The star will have become black holes.”(Stephen

Hawking, 1994, 108)

Another Important part of study of black holes include size of

black holes. There are at least two different ways to describe how big something is.

We can say how much massive the object is or how much space it takes up. There is

no limit to how much or how little mass a black hole can have. A typical mass for a stellar

black hole would be about 10 times the mass of Sun or about 10³¹ Kilograms (10³¹

means a 1 followed by 31 zeros after it ). It is also suspected that many galaxies

harbour extremely massive black holes at their centres. These are thought to weight

about a million times as much as sun.

Size of black holes, in terms of space also,

follows that , the more massive a black hole is , the more space it takes up. The

Schwarzschild radius (radius of horizon) and the mass of black holes bears a direct

relation between them. If one black hole weights ten times as much as another, its

radius is ten times as large.
Before proceeding further, lets just study

inverse of black hole. The equations of general relativity have an interesting

mathematical property; they are symmetric in time. That means that you can take any

solution to the equations and imagine that time flows backwards rather than forwards,

& you’ll get another valid solution. If this rule is applied to solution that describes

black holes, an object known as white hole is obtained. Since the black hole is a

region of space from which nothing can escape , the time reversed version of black

hole is region of space into which nothing can fall. Just as black holes can only sink

things in, a while hole can only spit things out. But, they aren’t actually found to exist

in nature. In fact, they almost certainly do not exist in nature, since there’s no way to

producing more.

Now, let’s ponder over an interesting thought, what would happen

to an object if it ever fell into black hole-

“A common suggestion is that if black hole is rotating , you can fall

through a little hole in space-time and out into another region of universe. This

obviously raises great possibility for space travel. Indeed, we will need something like

this if travel to other stars, bet alone to other galaxies, is to be a practical proposition

in the future. Otherwise, the fact that nothing can travel faster than light means the

round trip to the nearest star would take at least eight years. So much fir a weekend

break on Alpha Centauri! On the other hand , if one could pass through a black hole,

one might re-emerge(through a white hole) anywhere in the universe. Quite how to

choose your destination is not clear : you might set out for a holiday in Virgo and end

up in Crab Nebula.

I’m sorry to disappoint prospective galactic tourists, but this

scenario doesn’t work: if you jump into a black hole, you will get torn apart &

crushed out of existence.” (Stephen Hawking, 1994 , 104-5)

Let us consider an object falling into black hole. What would

happen to it? At first, there won’t be any gravitational force, since it’s a free fall. But

as the object gets closer & closer to centre of the hole, a tidal gravitational force starts

acting on it. In this, the part of object that is closer to centre than other part of object,

will be acted more by tidal force. So there will be difference in force acting at

different parts on the object. So, it will be stretched. These tidal forces will get more

& more intense as object gets closer to the centre & eventually they will rip the object

apart.

For a very large black hole, the one we’ve considered, object falling in, the

tidal forces are not really noticeable until it gets within about 600,000 km from centre.

But, if object is falling in smaller black hole, consider weighing as much as sun, the

forces will come into play at about 6000 km away from the centre and the object

would be torn apart even before it had crossed the horizon. That’s why we chose a
bigger black hole, we wanted object to survive at least until it gets inside! However,

whatever must be said, there are still debates on existence of black hole since as

earlier said , even light can’t return from a black hole. One can’t see a black hole

directly which means that we have to rely on indirect evidences. Suppose you’ve

found a region of space where you think there might be black hole. Then to check

authenticity of idea, we first need to check how much mass lies there in that region. If

you’ve found a large mass concentrated in small volume, and if the mass is dark, then

it’s a good guess that there’s a black hole there.

Physicist Tanmay Vachospati , Dejan

Stojkovic & Lawrence M. Krauss in the article, “Observation of incipient black hole

& the information loss problem”, have raised doubts against existence of black holes.

“ The Question that physicists set out to solve is :-

What happens when something collapses into black hole ? If all information is lost, it

defies the laws of Quantum Physics. Yet , in current thinking, once the matter goes

over the event horizon and forms a black hole, all information about it is lost.

“ (blog.case.edu)

However, two recent discoveries have been made that strongly

supports the hypothesis of existence of black hole. First, a nearby active galaxy was found

to have a "water maser" system near it's nucleus. Using advanced technique researchers

were able to map velocity within less than half a light year of the centre of the galaxy.It is

hard to imagine anything other than black hole there. Second discovery provides more

compelling evidence X-Ray astronomers have detected a spectral line from one galactic

nucleus that indicates presence of atoms near nucleus that are moving extremely fast. This

could be expected a black hole.
The next question in series is If a black hole existed would

it suck up all the matter in the universe? The simplest answer to this question is NO, 'cause

the black hole has a "horizon”, beyond which nothing can be affected as long as it is well

outside horizon. One common raised doubt is what if Sun became a black hole? Well, it just

won't happen, because only stars weighing more than twice the sun end their lives as black

hole. But we’d still like to assure that Sun has no intentions of becoming a BLACK HOLE,

at least for another five billion years!


Work Cited

1. Hawking , S.(1998) , A Brief History of Time , Berkshire (Great Britain),
Bantam Books, Inc.

2. Hawking , S.(1994) , Black Holes & Baby Universe, (Great Britain) Berkshire ,

Bantam Books, Inc.

3. White, M & Gribbin, J (1998) , Stephen Hawking : A Life in Science , London ,

Penguin Books, Inc.

4. http://blog.case.edu/case-news/2007/06/20/blackholes.html

5. http://cosmology.berkeley.edu/education/Bhfaq.html

6. http://en.wikipedia.org/wiki/black_holes.html

7. http://library.thinkquest.org/c0110484/content.php?id=31

8. http://rtfm.mit.edu

9. http://www.google.com

10. http://live.msn.com