Black holes !

Black holes are perhaps the most mysterious objects in the universe. In layman’s language, it can be said that a black hole is a body with gravitational pull so intense that not even light can escape from it thus making it ‘black’

So if the black hole is indeed ‘black’, how do you see it ? Well, it turns out that you can’t. In fact we have never actually observed a black hole in the same manner as we can view distant stars and galaxies. We can’t see them; but we can definitely predict their presence and detect their strange effects.

To get an understanding of these effects, we first need to visit one of the theories which changed the way we view our universe – Albert Einstein’s general relativity.

Einstein’s Tower Experiment

You throw a ball high up into the air vertically using only your physical strength. What would you expect will happen to the ball? A reasonable person would say the ball will go up for a certain amount of time before it comes to a halt and then eventually it will drop on the ground.

This happens so the kinetic energy(KE) of the ball (KE is highest at the point of release from the arm) is converted to gravitational potential energy(PE) when the ball is thrown up. The ball stops when all KE is converted to PE .Then while falling down, it converts all its PE to KE in the reverse process. All this is basic High school physics !

Here’s where things can get complicated though; what if you are shooting a beam of light from the surface of the earth vertically up? Would you expect light particles (photons) to lose some of their kinetic energy the same way that a ball would?

Turns out that if we assume that light will not be affected by gravity and lose its kinetic energy as it moves up, then using Einstein’s Energy- mass relationship we come to  strange consequences where extra energy is created! This violates the conservation of energy law – energy can neither be created nor destroyed. Therefore, our assumption that gravity does not affect photons must be wrong and calls for a correction. So we correct our mistake by showing that the photon loses energy when moving vertically up. This phenomenon is called Gravitational Redshift.

Now imagine an observer standing at the top of a tower – stationary w.r.t. ground (not free falling). Put a source of light at the surface of the earth and shoot a beam of light vertically up. The photons lose energy due to earth’s gravity. This means that the frequency of the light wave decreases due to the fact that Energy of photons = Planck’s constant*Frequency. As a consequence, wavelength increases (inversely proportional to freq.) and hence it is called redshift as increasing wavelength shifts towards the red part of the spectrum. The speed of light is a fundamental constant of the Universe, it does not vary.Therefore as the photon loses energy while climbing vertically up from the surface of the earth, the observer will see the wave of light redshifted depending on how high he is standing and the strength of the earth’s gravitation1

Check your clocks !

Imagine a clock built out of frequency of light wave and placed at the surface of the earth. As the beam of light shoots up it will be redshifted by gravity, meaning the frequency will decrease and the clock will seem to slow down from the observer’s point of view. The understanding of this phenomenon revolutionized the world of physics.

Black Holes and General Relativity equations

Einstein derived a set of complex equations popularly known as Einstein field equations to describe the geometry of the Universe and how it “curves” due to mass and energy. So, the way of representing this curved space is, a massive object will put a dent in the space-time fabric and light travelling from near the object will have to cover a longer path causing it to “bend” due to the mass of the object (gravitation).

The most extreme prediction of this theory is a black hole. Well, how do these strange objects come into existence ? They are formed mostly from the death of a star. A star goes through a long evolutionary process starting from just a gas cloud. When stars having masses much higher than our sun are in the last stages of their evolution, the star explodes( the phenomenon is called a supernova) and the remaining mass goes on contracting in size. Correspondingly its gravitational pull keeps on increasing until the stage arrives where not even light can escape from it. So this stage of a star is called a ‘black hole’ due to the fact that no light ever can escape it.

Now look at above figure representing a black hole and let us analyze it from the General relativity point of view. The black hole does not merely dent the space time, but it puts a hole in it called singularity. This singularity could be interpreted as a point (no dimension) where all the BH mass is squeezed into and has theoretically infinite gravity2

 

As a result of light having a finite speed, there may exist a gravitational field so strong that light coming from the mass creating the field will lose all its energy before reaching a stationary observer outside the gravitational field. Such a gravitational field is created by a Black Hole and the corresponding area (no escape zone for light) known as the event horizon is proportional to the Schwarzchild radius3(SR). Information from inside the event horizon cannot reach outside. This is because the speed of light is a fundamental limit that we know on how fast anything can be transmitted from one point to other.

Does that mean BH is a vacuum cleaner that sucks everything inside? If suddenly the Sun turns into a BH would the Earth be sucked inside? No! Things will orbit around the black hole just like they orbit around a star if they are moving fast enough outside the event horizon. If they are moving too slow near the BH gravitational well they will fall towards the center. If they are moving too fast they will get deflected but continue moving in the same direction until acted upon by some other force. Inside the event horizon all world lines lead to singularity!

Astronaut freezes in time !

Go back to tower experiment in the earlier section. This time imagine an observer standing outside the gravitational potential of the Black hole, beyond gravitational potential of BH – stationary w.r.t. the BH. An astronaut is free falling into the black hole. As the astronaut is getting closer and closer to the event horizon the light emitted by his suit is getting more and more redshifted when it reaches the external observer. Hence the astronaut’s clock appears to be moving slower and slower w.r.t. external observer’s clock. But this is only relative, the astronaut perceives his own time moving normally. Now this clock slows down until the astronaut reaches the event horizon at which point the slowing-down-factor approaches infinity, in other words the external observer sees the astronaut frozen in time at the event horizon!

From the astronaut’s (assuming he manages to survive the immense tidal forces created by BH) perspective, all light from outside reaching his eyes will be blueshifted (opposite of redshift, photon gains energy) increasing frequency of wave more and more as he approaches the event horizon. Hence he sees the external observer’s clock moving faster and faster (frequency increases). At the event horizon he sees the observer’s clock moving infinitely faster!

The world’s biggest lenses

Of course we cannot send a person inside a black hole to test these theoretical predictions. Strong tidal forces of the BH are more likely to just rip a person apart before even reaching the event horizon. Instead lets look at what we can observe with telescopes and light sensitive detectors as a result of black holes.

A fascinating phenomenon Black holes (or any massive object creating spacetime curvature for that matter) can produce is called “gravitational lensing”. Imagine a black hole obstructing our view of a further object in some direction in space. The light from this object will bend due to the black hole’s gravitational well – as we saw earlier, light takes longer path to travel due to the curvature in spacetime. This bending may lead to distorted image of the object in the background.  The nature of the distortion and how the image will appear depends upon the angle the lensing object makes with the distant object and an observer on earth. See image below4

Ever since the discovery of gravitational lenses, astronomers have been interested in studying them. These lenses apart from being fascinating may be helpful in making more accurate measurements of distant objects.

Goodbye, Newton?

So there it is, the expansion of physics from Newtonian or classical mechanics with its notion of absolute time to theory of Relativity which integrates 3D space and time into a 4-Dimensional fabric of space-time. Space time has changed the way we look at the universe and it’s workings.

So do we just discard Newton’s classical laws of physics? Absolutely not! Relativistic calculations are not always practical or fruitful in improving our level of accuracy in cases of small influence of gravity (or small velocities we are dealing with). Classical mechanics is still very useful in making several deductions in the field of astronomy.

Footnotes:
1. This has been experimentally verified by putting extremely sensitive atomic clocks at various heights from the surface of the earth and measuring the differences in time due to earth’s gravitational well.
2. Humans have a hard time imagining infinity. It can be said our physics is insufficient at this point to understand this gravitational singularity
3. The Schwarzschild radius is the radius of the event horizon surrounding a non-rotating black hole. If any object is compressed to a physical radius smaller than its Schwarzschild radius, then it will become a black hole. Formula for the Schwarzschild radius is Rs = 2 GM/c^2. M is the mass of the body, G is the universal constant of gravitation, and c is the speed of light.
4.In the formation known as Einstein’s Cross, four images of the same distant quasar appear around a foreground galaxy due to strong gravitational lensing
References
http://www.universetoday.com/33454/how-do-black-holes-form/
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