Black Holes Research and Report

To understand a black hole, you must first have an understanding of gravity in space. Imagine yourself on a trampoline; you make an indentation in the trampoline fabric. If someone was to roll a ball past you on the trampoline, it would begin to spiral towards you, down into the indent you have made. This is very similar to the way gravity works in space and time. The 'fabric of spacetime' is an imaginary mesh running through space (see right) which can be deformed and warped by the gravity of stars and planets.

This is the principle upon which black holes work.

A black hole essentially is an incredibly compact body which has warped space-time enough to make any escape from the force of gravity impossible. They are thought to be at the centre of galaxies, including our own Milky Way. As the name implies, a blackhole cannot emit or reflect any light; making them practically invisible. If enough mass is concentrated into a small enough region, the curvature of space-time becomes so harsh that nothing can continue to orbit stably; not even light.

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The ultimate fate of all incoming matter is to be destroyed in a singularity, a region of infinite density. The interior of a black hole is poorly understood because no form of information can ever leave. However new technologies are allowing us to receive a new phenomenon called hawking radiation, so this may be true for only a short period of time.

Black holes are formed by the gravitational collapse of a star, in which the pressure created by the core of the star becomes insufficient to resist its own gravity.

This causes the star to collapse in on itself, known as a supernova. If the star was of large enough mass (at least 10 times the mass of the sun, depending on the type of black hole), it will collapse to form a black hole.

Black hole 'anatomy'

* Singularity-lies at the centre of the black hole, where matter is crushed to infinite density. This means the mass of the black hole is compressed into an area with 0 volume.

* Ergosphere-a region located outside a rotating black hole. It drags spacetime around with it at a speed exceeding that of light.

* Event horizon-the boundary in spacetime. Due to the massive gravitational pull, an extremely strong deformation occurs in spacetime. This means that of all the possible paths a particle could take, none lead away from the singularity (see

diagram below).

Types of Black Hole

There are three main types of black hole; Supermassive, Intermediate-mass and Stellar mass. There are also micro or primordial black holes which were created in the very early universe, possibly at the big bang.

Type of black hole

Mass

Radius

Supermassive

105 - 109 x MSun

1.5 x 1012 m

Intermediate

103 x MSun

109 m

Stellar

10 x MSun

30 x 103 m

Micro

up to MMoon

up to 10-4 m

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Supermassive Black Holes - it is widely accepted in astronomy that at the centre of every galaxy in the universe, there is a Supermassive black hole. A good example of this is our very own galaxy, which contains a black hole of mass 2.6 million solar masses, or, 5.17x1036 kilograms.

Intermediate-mass Black Holes - they are roughly about 1000 times the mass of the sun as shown by the table above. There is less evidence for these types of black hole than for other types, but they are thought to be the cause of ultra luminous x-rays being emitted from nearby galaxies.

Stellar-mass - these black holes are easier to comprehend as they are about the same size as the Earth. It is difficult to distinguish between stellar black holes and neutron stars as the size between the stars that form them is very similar, but like all black holes the matter entering them emits x-rays, proving them to be one or the other.

Micro black hole - also known as quantum mechanical black holes, they are tiny hypothetical black holes which have not yet been discovered, but are a very possible occurence.

Finding the Radius of the Event Horizon

To find the radius of the event horizon of a black hole, physicists first need use equations of potential gravitational field strength and kinetic energy...

and...

The total energy of the object in question, in this case a black hole, can be found by summing up the kinetic and potential energies...

Now substituting in the equations we get...

We can then work out the escape velocity needed to escape the bodies gravitational field...

Eventually the equation can be rearranged for r...

The speed of light is used instead of v so that you can determine how close anything can get to the black hole before escape is impossible.

Finding the Mass of a Black Hole

For black holes with an orbiting companion star, astrophysicists use the speed of that star to work out the mass of the black hole. They can usually tell the star is orbiting a black hole because it gives out high energy x-rays. They must first use the principle of Doppler shift to work out the speed of the star. Doppler shift comes into effect when objects are moving, stretching or squashing the wavelengths of the light they give out. This gives us the velocity, v of the object.

Next we must find the radius of the black hole, again using the companion star. By using the time the star takes to complete one orbit, i.e. the circumference of a circle, and the speed it is travelling at (found using Doppler shift), the radius can be found...

Circumference of a circle = 2?r = velocity x time

Therefore...

A simple acceleration equation can be used to measure the gravitational field strength, as they are essentially the same thing...

The gravitational inverse square law can now be rearranged and used to find the mass of the black hole. We must also substitute 'a' for 'g'...

Hawking Radiation

At a quantum mechanical level, black holes should not be black they should glow due to a phenomenon called 'Hawking Radiation'. This unusual type of radiation consists of photons and neutrinos, as well as many other types of particles. The effect however, is undetectable in large black holes as they have huge amounts of hot gas falling into them, emitting much more radiation than the black hole itself. Conversely, for small black holes the hawking radiation would be significant, giving the black hole a moderate glow. This proves that black holes can be destroyed, and means that the black hole, if left 'starved' of matter would be depleted of energy. Einstein's equation, E=mc2, shows that energy is equal to mass, meaning the black hole will simply waste away and die in a catastrophic explosion.

Particle pairs, such as matter and antimatter are constantly being made everywhere in the universe, even at the very edge of the event horizon of a black hole. Usually, particles and antiparticles, when made, immediately annihilate one another. However at the event horizon, it is possible for one of the particles to 'fall in' before they have a chance to annihilate. The particle not absorbed can then be emitted as Hawking Radiation. This currently is only a theory though, and has yet to be proven, but scientists believe there is no reason why it should/could not happen.

What happens when black holes collide?

At this moment, there are currently 14 known black holes in the universe, the closest of which is 8000 light years away i.e. 8x1019 meters away. However, it is predicted that there are many more undiscovered black holes. Scientists have spotted two supermassive black holes which are very close to each other, and if these ever came close enough that they could not escape each other's gravity, they would collide. Although this has never been witnessed before, theoretical models predict that they would spiral towards each other and eventually merge together to form one, larger black hole. This occurrence would be enormously powerful and send gravitational waves through space-time. Gravitational waves are a fundamental prediction in Einstein's theory of general relativity, but have never been directly observed or detected in space.

Gravitational Lensing

A gravitational lens is an occurrence only caused by black holes and other immensely heavy objects. It occurs when the object, say a black hole comes in between the observer and a very bright light source such as a quasar. A quasar is a light source, such as an active core of a distant galaxy, which sends out radio waves and other forms of energy. The light produced by the quasar is bent (see right) towards us by gravity from all angles relative to the black hole, causing us to see multiple images of the quasar. If the obstructing object came directly and symmetrically between the observer and the quasar, a perfect ring of quasars would be seen, as the light is refracted from all angles perfectly.

However if the black hole was slightly off centre, the images of the quasar formed would seem to be different distances away from the actual quasar, as shown below.

Here's an example...

The size of the Einstein ring can be found using this equation:

where:

* ?E = Einstein radius in radians

* G = 6.64 x 10-34

* M = mass of black hole (lens)

* c = speed of light

* dLS = the angular diameter distance between lens and light source

* dL = the angular diameter distance from the lens

* dS = the angular diameter distance from the source

Einstein Rings

An Einstein ring is a deformation of light by gravitational lensing, due to a crossing path of a massive gravitational body such as a galaxy or black hole and a star or planet. The light is bent by the gravity and forms a visible circle around the black hole. If you were to stand in the ring and as long as you, the lens and the source were all aligned, you would be able to see yourself from behind.

Astrophysicists hope that Einstein rings will help their search for dark matter (which is believed to make up 90% of our universe) and help them to understand it more fully.

Evaluation

Throughout this assignment I have learnt many things about the mysterious Black Hole. From what I have found, the physics behind them looks extremely complex and the theory is sometimes difficult to comprehend. But with new technology and theories advancing, the truth about black holes can only become clearer.

References

http://en.wikipedia.org/wiki/Black_hole

I used this website as a source for a large portion of the information involving the properties and formation of the black hole, as well as other useful facts. Although Wikipedia can sometimes be inaccurate, I feel that the information provided was simple, yet managed to give a great insight into the areas it explains.

http://hubblesite.org/explore_astronomy/black_holes/

This website was used for the section, 'What happens when Black Holes collide?' and was very useful as it is used by the general public of all intelligences and ages, making it easy for me to understand the things I was writing about.

http://imagine.gsfc.nasa.gov/docs/science/know_l2/black_holes.html

I used this website to find out more about what black holes actually are. I trusted this source as it came from NASA, a very reliable and well known organisation.

http://cosmology.berkeley.edu/Education/BHfaq.html

This website was used to help me explain what would happen if a black hole was left starved of matter. It also helped me to gain knowledge of what is believed to happen to matter as it falls into a black hole. It seemed like a trustworthy source as lots of information was given, as well as a lot of detail.

http://design.lbl.gov/education/blackholes/index.html

To help me explain how the equation for the radius of the event horizon was derived, the above website was extremely helpful as it gave a full breakdown as to where each part of the equation came from and how this was so. The site has links to the U.S Department of Energy, so again is a fairly dependable source.

A2 Advancing Physics Book - Institute of Physics

This book was given to me by my Sixth Form and was a great source of background reading, as well as the main basis for my 'Mass of a Black Hole' section. It was written by the Institute of Physics (IOP) so yet again is a very secure resource.