GRAVITATIONAL WAVES theory explaination etc

1. GRAVITATIONAL WAVES &
LIGO
-Vaid P Kulkarni
Mechanical A
35

2. • Gravitational waves are 'ripples' in space-time caused by some of the most violent and
energetic processes in the Universe.
• Albert Einstein predicted the existence of gravitational waves in 1916 in his general theory
of relativity.
• Einstein's mathematics showed that massive accelerating objects (such as neutron stars or
black holes orbiting each other) would disrupt space-time in such a way that 'waves' of
undulating space-time would propagate in all directions away from the source.
• These cosmic ripples would travel at the speed of light, carrying with them information
about their origins, as well as clues to the nature of gravity itself.
• The strongest gravitational waves are produced by cataclysmic events such as colliding
supernovae (massive stars exploding at the end of their lifetimes), and colliding neutron
• Other waves are predicted to be caused by the rotation of neutron stars that are not perfect
possibly even the remnants of gravitational radiation created by the Big Bang.

3. The animation below illustrates how gravitational waves are emitted by two neutron stars as they orbit each other and then coalesce
(form one mass or whole) (credit: NASA/Goddard Space Flight Center). Note that gravitational waves themselves are invisible. They
are made visible here to illustrate their propagation away from the source.

4. • Though Einstein predicted the existence of gravitational waves in 1916, the first proof of their existence didn't arrive until 1974,
20 years after his death.
• In that year, two astronomers using the Arecibo Radio Observatory in Puerto Rico discovered a binary pulsar, exactly the type
of system that general relativity predicted should radiate gravitational waves.
• Knowing that this discovery could be used to test Einstein's audacious prediction, astronomers began measuring how the
stars' orbits changed over time.
• After eight years of observations, they determined that the stars were getting closer to each other at precisely the rate
predicted by general relativity if they were emitting gravitational waves.
• Since then, many astronomers have studied pulsar radio-emissions (pulsars are neutron stars that emit beams of radio waves)
and found similar effects, further confirming the existence of gravitational waves.
• But these confirmations had always come indirectly or mathematically and not through direct contact.
The given diagram is representing
binary pulsar in a artist’s view.

5. • All of this changed on September 14, 2015, when LIGO physically sensed the undulations in spacetime caused by gravitational
waves generated by two colliding black holes 1.3 billion light-years away.
• LIGO's discovery will go down in history as one of humanity's greatest scientific achievements.
• While the processes that generate gravitational waves can be extremely violent and destructive, by the time the waves reach
Earth they are thousands of billions of times smaller!
• In fact, by the time gravitational waves from LIGO's first detection reached us, the amount of space-time wobbling they generated
was a 1000 times smaller than the nucleus of an atom!
• Such inconceivably small measurements are what LIGO was designed to make.
LIGO-Laser Interferometer
Gravitational Wave Observatory

6. WHAT ARE GRAVITATIONAL WAVES
IN SIMPLE LANGUAGE ?
• A gravitational wave is an invisible (yet incredibly fast) ripple in space. Gravitational waves travel at the
speed of light (186,000 miles per second).
• These waves squeeze and stretch anything in their path as they pass by.
• Einstein predicted that something special happens when two bodies—such as planets or stars—orbit
each other.
• He believed that this kind of movement could cause ripples in space. These ripples would spread out like
the ripples in a pond when a stone is tossed in.
• Scientists call these ripples of space gravitational waves.

7. HOW MASS BENDS SPACE

8. What causes gravitational waves?
The most powerful gravitational waves are created when objects move at very high speeds. Some
examples of events that could cause a gravitational wave are:
•when a star explodes asymmetrically (called a supernova)
•when two big stars orbit each other
•when two black holes orbit each other and merge
An artist’s animation of
gravitational waves
created by the merger of
two black holes. Credit:
LIGO/T. Pyle
But these types of objects that
create gravitational waves are
far away. And sometimes,
these events only cause small,
weak gravitational waves. The
waves are then very weak by
the time they reach Earth. This
makes gravitational waves
hard to detect.

9. How do we know that gravitational waves exist?
In 2015, scientists detected gravitational waves for the very first time. They used a very sensitive
instrument called LIGO (Laser Interferometer Gravitational-Wave Observatory). These first gravitational
waves happened when two black holes crashed into one another. The collision happened 1.3 billion years
ago. But, the ripples didn’t make it to Earth until 2015!
LIGO is made up of two
observatories: one in Louisiana
and one in Washington
(above). Each observatory has
two long “arms” that are each
more than 2 miles (4
kilometers) long. Credit:
Caltech/MIT/LIGO Lab

11. How are gravitational waves detected?
When a gravitational wave passes by Earth, it squeezes and stretches space. LIGO can detect this
squeezing and stretching. Each LIGO observatory has two “arms” that are each more than 2 miles (4
kilometers) long. A passing gravitational wave causes the length of the arms to change slightly. The
observatory uses lasers, mirrors, and extremely sensitive instruments to detect these tiny changes.

12. LIGO's Interferometer
At their cores, LIGO's interferometers are Michelson Interferometers, the same sort of device that was invented in the 1880's:
•They are L-shaped (not all interferometers are this shape)
•Mirrors at the ends of the arms reflect light in order to create an interference pattern called 'fringes'
•A device called a photodetector measures these fringes, revealing minute details of the objects or phenomenon being studied
But this is where the similarities end. The size and added complexity of LIGO's
interferometers are far beyond anything the world's first interferometers could
have achieved.
The first most obvious difference between a typical Michelson interferometer and
LIGO's interferometers is its scale. With arms 4km (2.5 mi.) long, LIGO's
interferometers are by far the largest ever built. (By contrast, the interferometer
Michelson and Morley used in their famous experiment to study the "aether" had
arms about 1.3m long). The scale of LIGO's instruments is crucial to its search
for gravitational waves. The longer the arms of an interferometer, the smaller the
measurements they can make. And having to measure a change in distance
10,000 times smaller than a proton means that LIGO has to be larger and more
sensitive than any interferometer ever before constructed.

13. While 4km-long arms seems pretty huge, if LIGO's interferometers were simple Michelson's, they would still be too short to enable the
detection of gravitational waves. And of course there are practical limitations to building such a precision instrument much larger than
4km.
Longer is Better The paradox was solved by altering the design of the Michelson to
include something called "Fabry Perot cavities". The figure at left
shows a basic Michelson design modified to include such cavities.
An additional mirror is placed in each arm near the beam splitter
(the box on the 45-degree angle), 4km from the mirror at the end of
that arm. This 4km-long space comprises the Fabry Perot cavity.
After entering the instrument via the beam splitter, the laser in each
arm bounces between its two mirrors about 300 times before being
merged with the beam from the other arm.
Basic Michelson interferometer with Fabry Perot cavities. Additional mirrors are
inserted near the beam splitter to facilitate multiple reflections of the laser,
containing it within the interferometer and increasing the distance traveled by the
beams. This greatly increases LIGO's sensitivity to the smallest changes in arm
length.

14. These reflections serve two functions:
• It builds up the laser light within the interferometer, which increases LIGO's sensitivity (more photons also makes LIGO more
sensitive)
• It increases the distance traveled by each laser from 4km to 1200km thereby solving our length problem! (The light in
Michelson's original interferometer only traveled 11 meters.)
• Since we know that the longer the arms of an interferometer, the more sensitive the instrument is to vibration, this
design significantly increases LIGO's sensitivity and enables it to detect changes in arm length much smaller than a proton--the
size of changes expected to be caused by a gravitational wave. And thanks to Fabry Perot cavities, LIGO can achieve this
sensitivity with arms just 4km long.
• There is an analogous effect in optical telescopes. Increasing the focal length of a telescope (also how far the light travels
between mirrors or lenses before reaching your eye) not only increases the magnification achievable by any given eyepiece, but
it also amplifies the smallest vibrations in the telescope. In a telescope, these vibrations are unwanted.
• LIGO, on the other hand, was designed to feel them, and with arms effectively 1200km long, LIGO's interferometers can amplify
the smallest conceivable vibrations enough that they are detectable and measurable.

15. We Need More Power!
Length isn't the only limiting factor in LIGO's sensitivity. Laser power is also a consideration.
the interferometer's sensitivity, increasing laser power also enhances its performance. While
changes in arm length, increasing laser power results in increasing the interferometer's
laser photons merge from each arm, the sharper the fringes that are measured by the
But there's a problem here too. LIGO's laser first
enters the interferometer at about 40 Watts, but
it needs to operate closer to 750kW if it has any
hope of detecting gravitational waves. Here we
have another paradox. Just as it would be
impossible to build a 1200km-long
interferometer, building a laser with this initial
power is a practical impossibility.
Once again, LIGO uses mirrors to solve this
dilemma. They are called Power Recycling
Mirrors. The figure shows schematically where a
power recycling mirror is located inside each
interferometer.
Basic Michelson with Fabry Perot cavities and Power
Recycling mirror. LIGO's interferometers actually use
multiple power recycling mirrors but for simplicity only
one is shown in the diagram.

16. • Inside the interferometer, light from the laser passes through the transparent side of a power recycling mirror to the beam splitter
and then on to the arms of the interferometer. The beam splitter is like those one-way mirrors in police dramas: half the light
comes out, the other half is reflected back into the room.
• The instrument's alignment and mirror coatings, and even quantum mechanics, ensure that nearly all of the laser light entering the
arms follows a path back to the reflective side of the power recycling mirror rather than to the photodetector.
• As laser power is constantly entering the interferometer, the power recycling mirror continually reflects the laser light that has
traveled through the instrument back into the interferometer (hence 'recycling’).
• This process greatly boosts the power of the laser beam inside the Fabry Perot cavities without the need to generate such a
powerful laser beam at the outset.
• The boost in power generated by power recycling results in a sharpening of the interference fringes that appear when the two
beams are superimposed--fringes which will tell scientists if a gravitational wave has passed.
• The sharper the fringes, the easier it becomes to identify the tell-tale signs of gravitational waves.

17. NOT QUITE THERE YET!
• Two other modifications make LIGO's interferometers unique and able to
make the world's smallest measurements. First, they also possess 'signal
recycling' mirrors, which, like power recycling, enhance the signal that is
received by the photodetector. And second, LIGO's interferometers were
constructed with extraordinary mechanisms to damp out unwanted
vibrations (noise) making it easier for scientists to weed out vibrations
caused by gravitational waves. LIGO's seismic isolation system is discussed
in much greater detail in LIGO Technology.
• With these modifications, LIGO's interferometer is known as a Dual
Recycled, Fabry-Perot Michelson -- but at its heart, it is still a Michelson
interferometer.
https://www.ligo.caltech.edu/page/ligo-technology
LIGO TECHNOLOGY 

18. Einstein’s equations.
• In 1905, one of Einstein’s achievements was to establish the theory of Special Relativity from 2 single
postulates and correctly deduce their physical consequences (some of them time later). The essence of
Special Relativity, as we have seen, is that all the inertial observers must agree on the speed of light “in
vacuum”, and that the physical laws (those from Mechanics and Electromagnetism) are the same for all of
them. Different observers will measure (and then they see) different wavelengths and frequencies, but the
product of wavelength with the frequency is the same. The wavelength and frequency are thus Lorentz
covariant, meaning that they change for different observers according some fixed mathematical
prescription depending on its tensorial character (scalar, vector, tensor,…) respect to Lorentz
transformations. The speed of light is Lorentz invariant.
• By the other hand, Newton’s law of gravity describes the motion of planets and terrrestrial bodies. It is all
that we need in contemporary rocket ships unless those devices also carry atomic clocks or other tools of
exceptional accuracy. Here is Newton’s law in potential form:

19. In the special relativity framework, this equation has a terrible problem: if there is a change in the mass density
rho, then it must propagate everywhere instantaneously. If you believe in the Special Relativity rules and in the
speed of light invariance, it is impossible. Therefore, “Houston, we have a problem”.
Einstein was aware of it and he tried to solve this inconsistency. The final solution took him ten years .

20. WHAT IS EINSTEIN FIELD EQUATION?
Where,
Gμ𝜐 is the Einstein tensor which is given as Rμ𝜐-½ Rgμ𝜐
Rμ𝜐 is the Ricci curvature tensor
R is the scalar curvature
gμ𝜐 is the metric tensor
𝚲 is a cosmological constant
G is Newton’s gravitational constant
c is the speed of light
Tμ𝜐 is the stress-energy tensor

32. LAST BUT NOT THE LEAST!!!!!!
THIS IS ONLY THE DAWN
OF ASTROPHYSICS OF
GRAVITATIONAL WAVES