Gravitational Waves are the “ripples” or ‘disturbances” in the fabric of space-time caused due to the most energetic astrophysical events in the universe like the merger of black holes, neutron stars, supernovae explosions, etc.

## Gravitational waves

were first predicted in the year of 1916 by Einstein in his General Theory of Relativity.

General relativity or GR is “THE” theory of gravity. So far our best understanding of gravity is through Einstein’s theory of relativity.

Einstein proposed his theory of relativity into two parts-

1. Special Theory of Relativity
2. General Theory of Relativity

It is important for us to have some basic ideas on what these theories actually meant.

Special Theory of Relativity

originally proposed by Albert Einstein in a paper published 26 September 1905 titled “On the Electrodynamics of Moving Bodies“.  A translation that has often been used is “restricted relativity”; “special” really means a “special case”.

In physics, special relativity is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time. In  Einstein’s original pedagogical treatment, it is based on two postulates:

1. The laws of physics are invariant (i.e., identical) in all inertial systems (i.e., non-accelerating frames of reference).
2. The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.

So there is a speed limit in the universe, which is the speed of light and the laws of physics conspires that nothing ever goes faster than the speed of light. We don’t notice this in our daily life because light moves really fast! almost 299792458 m / s!!

Now if we really think about it a little bit, its really weird.

Say, there is a speed limit in the motorway and it is 80 mph. Just imagine your car doesn’t go above 80 mph. So the speed limit of 80 mph is the motorway is relative to a person who is standing still on the side of the motor way.

But what about the people in the other side of the lane ?

The people who are there in their cars, driving down at 80 mph. From their perspective the car , that is coming towards them doesn’t look a like coming at 80 mph, they look as if its coming at 160 mph. Since the relative velocities add up that way.

∴ It is 80 mph(your velocity ) + 80(of the car coming towards you)= 160 mph

So that is how fast the cars are moving towards each other.

You would think, the same thing must be true. If i take a torch and shine it at you , the light leaves my hand and travels towards you at the speed of light, which is 299792458 m / s.

Now imagine , you were running towards me at half the speed of light at 149896229 m/s(obviously thats a physical exertion!! and since we are speaking in terms of mathematics and number we can pretend all that).

How fast do you see the light coming at you?

The simple , common sense answer would be (299792458 + 149896229)m/s = 449688687 m/s !!!

Okay so, let me warn you, common sense is not always a great thing to understand the way our universe works. And obviously 449688687 m/s is not the answer.

The answer is no matter how fast you run towards me, you will always see the light travelling towards you at the same speed that light travels in, 299792458 m/s .

Infact the way we were simply adding up the velocities isn’t the exact thing to do. There is a slight and a very small correction to that.

The correct formula to calculate this is , what Einstein came up with in 1905 ,

The denominator term was the correction factor.

So when v= c = 299792458 m/s , then we get,

∴ No matter how fast you run towards light (maximum being c, the speed of light) you always see it coming towards you at exactly the same speed 299792458 m / s.

So it was established that nothing can travel faster than the speed of light.

But, there was a problem. And the problem was, he realized that if his theory was correct then Newtons theory of gravity could not be correct. So they both be couldn’t right at the same time.

The Earth goes around the sun in a fixed elliptical orbit.

If the sun wasn’t there , there would be no reason for the earth to continue around its orbit. It would move through a straight line in space.

So Einstein’s question was, when does the earth realize, that it should stop going in a circle and start travelling in s straight line?  When  does the effect of gravity get communicated ? or how long does it take for this effect of gravity to be communicated from the sun to the earth?

According to Newtons theory and equations, there is no time-delay. According to him the earth would immediately go in a straight line.

But Einstein had already figured out that nothing can travel faster than the speed of light, not even the effect of gravity.

So Einstein was pretty sure that the earth would continue to move in its orbit for about 8 mins ( since light form the sun also takes 8 mins to come to the earth) and then only it will realize that the sun isn’t there anymore and will drift off in a straight line.

So we now know that the effect of gravity also travels at the speed of light , so similarly the gravitational waves also travel through space at the speed of light.

Basically in relativistic sense, the “speed of gravity” refers to the speed of a gravitational wave, which is the same speed as the speed of light (c) which was predicted by General Relativity and confirmed by observation of the GW170817 neutron star merger.

Now lets study a bit about Spacetime Fabric and the exact nature of Gravitational Waves,

According to Einstein space-time is just like a fabric, having the exact same properties as that of a fabric of cloth. It bends and wraps just like a fabric does.

Empty space isn’t passive its dynamic. If something happens to space it responds to it.

This is pretty much a visual representation of how the empty space time fabric looks like.

Distances in this flat space can be calculated as :

which is just simple pythagoras .

However when we put something in this empty space it responds to it, by wrapping and bending around it and causing other objects to revolve around it.

#### The Mathematics of Curved space

So Einstein realized that distances in curved space time were simply not calculated the way that the Greek’s thought it ( by pythagoras ) but its actually much complicated.

So what are the Gravitational Wave equations?

We have a relatively flat space.

A ripple represents a small deviation from this flat spacetime metric.

We use “h” to represent these small deviations. Solutions to Einstein’s equations show that a gravitational wave metric oscillates sinusoidally just like light.

It also travels at the same speed , of light at 299792458 m/s.

As the wave moves down the z-axis

planes at different time experiences different values from the metric used to measure distance on the plane.This makes the wave a transverse wave just like light.

There are two possible polarization for gravitational waves, just like light waves

1. h+(h-plus) polarization. For the action along the x and y axes.

2. hx(h-cross) polarization ( for action along the diagonal)

So these modes of polarizations basically causes the planes to expand from one axis and contract from the other

So a increase of 1 m (say) in x-axis will cause a decrease of 1 m(say) in the y-axis.

Therefore when describing a gravitational wave we can now be more precise than saying “its a ripple in space time”

A gravitational wave is an oscillating polarized metric that operates in the plane perpendicular to the direction in which the waves move through spacetime at the speed of light. And for all the objects(including spacetime) that it encounters is stretched and squeezed in various directions.

so when a gravitational wave passes through the earth it stretches and squeezes it as shown.

What causes Gravitational Waves?

As mentioned above any mass in the fabric of space time causes it to bend according to the mass of the object.

Gravitational waves are produced when these masses accelerate , changing the distortion of spacetime. Everything with mass or energy can make gravitational waves.

If you and I started to dance around each other we would also cause gravitational waves in the fabric of space-time, but these would be extremely small and practically undetectable.

Now as we saw in the article of standard model , that gravity is very weak in the scale of other forces in the universe, so you need something really massive moving at very fast velocities to make the big ripples that we can detect.

so events like :

causes the gravitational waves which are detectable here on earth.

How where the Gravitational waves detected ?

At about 6 o clock in the morning on September 14th, 2015 scientists witnessed something, no human had ever seen. Two black holes colliding. Both about 30 times as massive as our sun. They had been orbiting each other for millions of years. As they got closer together they circled each other faster and faster. Finally they collided and merged into a single even bigger black hole. A fraction of a second before they had crashed, they had sent a  vibration across the universe at the speed of light. And on earth billions of years later a detector called LIGO ( Laser Interferometer Gravitational-Wave Observatory)  picked it up.

The signal only lasted for a fifth of a second and was the detectors first observation of gravitational waves.

Now the question is how would you observe these vibrations of ripple in space?

If the space between you and me stretched or compressed we wouldn’t notice it if we hadn’t made marks in our metaphorical rubber sheet. For example using equally spaced rocks, because these marks would also get stretched for your part.

But luckily there is one rule that doesnt get stretched. One made using the speed of light. If the space between two points get stretched then light will take longer to go from one point to the other. And if the space gets squeezed , then light will take lesser time to go from one point to the other.

This is the underlying principle used in the LIGO  experiments to detect the gravitational waves.

Just to be certain that , that the ripples detected were gravitational waves and not any other environmental disturbances two observatories were created in reasonably quite locations.

The detected waves(of the black hole merger) looked and sounded like:

Now how are these waves actually detected in LIGO?

As the ripple in space time passes the earth it causes the earth to squeeze and stretch ever so slightly.

However, the effect of this squeezing and stretching will be just a mere fraction of the diameter of an atom.

That makes it very difficult to detect.

LIGO has 4 km long tunnels and it uses lasers to measure the changes in the distance between the ends of the tunnel. When a gravitational wave comes through it stretches space in one direction and squeezes space in the other direction. By measuring the interference of the lasers as they bounce between the different points, physicist can measure very precisely whether the space in between has stretched or compressed. And the precision of this is incredible.

When there is no disturbance in the fabric of spacetime, the two light waves undergo perfect destructive interference and no interference pattern is recorded in the sensor. However when a gravitational wave passes by it causes the earth to get stretched and squeezed ever so slightly which in turn causes the 4km long tubes to expand and contract causing the crests and the troughs of the two waves to get dis-aligned and therefore form a interference pattern.

To detect a gravitational wave you need to be able to tell , when something changes in length in few parts by a fraction 10^23.

Its like being able to tell a stick 1 secstillion meters has shrunk by 5mm

The effect of gravitational wave is so minuscule and easily confused with random noise, you need a smart data analysis technique. Scientists hope to identify the patterns of gravitational waves by comparing the wiggles in measuring in the  experiment to the wiggles they measure during gravitational waves. Thats like trying to identify a song being hummed in a super load rock concert.

CONCLUSION

Imagine your whole life, you have been deaf until one day you start hearing. You’d be able to explore the universe in this whole new way. Thats why detecting gravitational waves is so significant, its a completely new way of studying the universe. Anytime there is new way to investigate the universe we discovered things we didnt expect. Its really about looking for new things we didnt know existed , examining the extreme edges of our knowledge of physics and testing our theories about how the universe works.

More articles on gravitational wave and black hole merger will be coming soon.

I would highly recommend few books that would really help you to know  in depth about black holes  and much more regarding the cosmos:

Cheers!

#### Mayukh

I am Mayukh Bagchi. 4th year Undergraduate Engineering student at SRM University , physics and in general Astrophysics is my passion and I want to pursue the same. This blog is dedicated to serve the community with honest and clear insights to the cosmos.

#### Mayank Soni · June 25, 2018 at 4:49 pm

How can you say that speed of gravity equals the speed of light?

#### Mayukh · June 25, 2018 at 5:02 pm

see basically in relativistic sense, the “speed of gravity” refers to the speed of a gravitational wave, which is the same speed as the speed of light (c) which was predicted by General Relativity and confirmed by observation of the GW170817 neutron star merger.

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