General Relativity and Gravitation:

Presented By1.B.Asmitha

2.A.ChinnaDuraiRageshFrom

M.D.T.Hindu college

Introduction:

When the word “PHYSICS” be pronounced, suddenly two names were strikes on our Mind they are

Sir Isaac Newtonand

Albert Einstein

Why???????????

Because they made great impact on the field physics

Newton is famous for his Gravitional laws Einstein is famous for his Relativity theories These two are unnegligible in physics

What is the relation between them?

GRAVITY

How………………………….?

Sir Isaac Newton

Universal Law of Gravitation Any two bodies in the

Universe attract each other with a force proportional to the masses and inverse of the square of the separation, along the line joining them.

F = Gm1m2/r2

Sir Isaac Newton could describe gravity but couldn’t explain it.– For 200 years, science didn’t

have an explanation for gravity until a clerk in a patent office in Switzerland named Albert Einstein…

Some defects!

By the beginning of the 20th century, Newton's law of universal gravitation had been accepted for more than two hundred years as a valid description of the gravitational force between masses.

In Newton's model, gravity is the result of an attractive force between massive objects.

Although even Newton was troubled by the unknown nature of that force, the basic framework was extremely successful at describing motion.

Einstein.,,,,,

Albert Einstein was a German-born theoretical physicist

He developed the general theory of relativity,

It is one of the two pillars of modern physics

Cont…….,,

Einstein's work is also known for its influence on the philosophy of science

Einstein is best known in popular culture for his mass–energy equivalence formula E = mc2

Introduced his Special Theory of Relativity in 1905 and

His General Theory of Relativity in 1915.

<Corrections>

The first showed that Newton's Three Laws of Motion were only approximately correct, breaking down when velocities approached that of light.

The second showed that Newton's Law of Gravitation was also only approximately correct, breaking down when gravitation becames very strong.

Ether……..

Light also needs a Medium to propagate. (assumption)

This Hypothetical Medium was named as Luminiferous Ether.

Michelson and Morley Conducted an Experiment for proving the Existence of Ether.

Evolved after the failure of Michelson Morley Experiment.

The negative results were explained successfully by an German-American Physicist, Albert Einstein (1879-1955).

Special Theory of Relativity Special theory was proposed on 1905 It is for non accelerated reference frame A Reference Frame is the point of View, from

which we Observe an Object. A Reference Frame is the Observer it self, as the

Velocity and acceleration are common in Both.

Postulates of Special Theory of Relativity* “The Laws of physics are same in all Inertial

Frame of reference”

“The Speed of Light in free space has the same value in all Inertial Frames.”

The Major Consequences To This Theory are:-

Length Contraction

Mass Expansion

Time Dilation

Length Contraction

“It is the phenomenon of Shortening of Length which is in the relative motion with respect to the observer”

Thus the length of a body appearing to an observer depends upon the relative velocity of the body with respect to the Observer.

It is given by l = lo /(1-v 2/c 2) 0.5

Mass Expansion , E = mc2

As an object's speed approaches the speed of light from an observer's point of view, its relativistic mass increases thereby making it more and more difficult to accelerate it from within the observer's frame of reference.

The energy content of an object at rest with mass m equals mc2. Conservation of energy implies that, in any reaction, a decrease of the sum of the masses of particles must be accompanied by an increase in kinetic energies of the particles after the reaction. Similarly, the mass of an object can be increased by taking in kinetic energies.

E = mc2

Time Dilation

Time Dilation is the phenomenon of slowing down of a clock , as determined by an observer who is in relative motion with the Clock.” **

As it is an relative thus the Extent of Dilation depends upon

the Relative Velocity of the clock w.r.t. the observer.

It is an very important consequence of the Special Theory of Relativity .And is given by t = to/(1-v 2/c 2) 0.5

General theory of Relativity General relativity is a theory of gravitation that

was developed by Albert Einstein between 1907 and 1915. According to general relativity, the observed

gravitational effect between masses resultsfrom their warping of spacetime.

Facts…………………

General Relativity, or GR, was created in order to better understand gravity

It has helped us to answer why gravity exists General Relativity has many predictions most of

which have been verified by experiment with amazing accuracy

Facts…………..,

The special theory of relativity encompasses inertial frames of reference moving at uniform relative velocities

Einstein asked whether or not systems moving in nonuniform motion with respect to one another could be relative and came up with the idea of general relativity

The History of GR Developed between 1907 and 1915 The beginnings of GR germinate in 1907 with Einstein’s

thought experiment concerning a free-falling observer that he called the happiest thought of his life: "For an observer falling freely from the roof of a house, the gravitational field does not exist"

The History of GR

1907- published first paper applying SR to accelerating reference frames that also predicted gravitational time dilation

1911- published paper predicting gravitational lensing 1912- Einstein was focused on formulating a theory of

spacetime that was purely geometrical

The History of GR

By 1915 Einstein had developed what are known as the Einstein Field Equations

General Theory of Relativity published in Annalen der Physik in 1916

Basic concepts

General relativity is the extension of special relativity. It includes the effects of accelerating objects and their mass on spacetime.

As a result, the theory is an explanation of gravity. It is based on two concepts: (1) the principle of

equivalence, which is an extension of Einstein’s first postulate of special relativity and (2) the curvature of spacetime due to gravity.

Principle of Equivalence The principle of

equivalence is an experiment in noninertial reference frames.

Consider an astronaut sitting in a confined space on a rocket placed on Earth. The astronaut is strapped into a chair that is mounted on a weighing scale that indicates a mass M. The astronaut drops a safety manual that falls to the floor.

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Cont…………….

Now contrast this situation with the rocket accelerating through space. The gravitational force of the Earth is now negligible. If the acceleration has exactly the same magnitude g on Earth, then the weighing scale indicates the same mass M that it did on Earth, and the safety manual still falls with the same acceleration as measured by the astronaut. The question is: How can the astronaut tell whether the rocket is on earth or in space?

Principle of equivalence: There is no experiment that can be done in a small confined space that can detect the difference between a uniform gravitational field and an equivalent uniform acceleration.

Spacetime Curvature of Space Light bending for the Earth observer seems to violate the

premise that the velocity of light is constant from special relativity. Light traveling at a constant velocity implies that it travels in a straight line.

Einstein recognized that we need to expand our definition of a straight line.

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Cont………………………………..

The shortest distance between two points on a flat surface appears different than the same distance between points on a sphere. The path on the sphere appears curved. We shall expand our definition of a straight line to include any minimized distance between two points.

Thus if the spacetime near the Earth is not flat, then the straight line path of light near the Earth will appear curved.

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Einstein's geometric gravity

In Einstein's theory ofgeneral relativity, gravity is a distortion of space-time.Particles follow the straightestpossible paths in that space-time. But because space-time is now distorted, even on those straightest paths, particles accelerate as if they were under the influence of what Newton called the gravitational force.

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Consequence of general theory

Gravitational time dilationgravitational time delayGravitational waves

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Gravitational time dilation

Assuming that the equivalence principle holds, gravity influences the passage of time

Light sent down into a gravity well is blueshifted,whereas light sent in the opposite direction is redshifted; collectively, these two effects are known as the gravitational frequency shift.

More generally, processes close to a massive body run more slowly when compared with processes taking place farther away; this effect is known as gravitational time dilation

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gravitational time delay

General relativity predicts that the path of light is bent in a gravitational field;

light passing a massive body is deflected towards that body. This effect has been confirmed by observing the light of stars or distant quasars being deflected as it passes the Sun

gravitational time delay (or Shapiro delay), the phenomenon that light signals

take longer to move through a gravitational field than they would in the absence of that field

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Gravitational Waves

Fluctuation of spacetime curvature that is propagated as a wave

Radiates away from accelerating bodies Carries energy away from source Predicts that two massive bodies rotating about

their center of mass will loose energy in the form of gravity waves and the orbit will decay

Tests of General RelativityBending of Light During a solar eclipse of the sun by the

moon, most of the sun’s light is blocked on Earth, which afforded the opportunity to view starlight passing close to the sun in 1919. The starlight was bent as it passed near the sun which caused the star to appear displaced.

Einstein’s general theory predicted a deflection of 1.75 seconds of arc, and the two measurements found 1.98 ± 0.16 and 1.61 ± 0.40 seconds.

Since the eclipse of 1919, many experiments, using both starlight and radio waves from quasars, have confirmed Einstein’s predictions about the bending of light with increasingly good accuracy.

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Applications

Gravitational lensingGravitational RedshiftCosmologyBlack Hole

Gravitational Lensing

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When light from a distant object like a quasar passes by a nearby galaxy on its way to us on Earth, the light can be bent multiple times as it passes in different directions around the galaxy.

Perihelion Shift of Mercury The orbits of the planets are ellipses, and the point closest

to the sun in a planetary orbit is called the perihelion. It has been known for hundreds of years that Mercury’s orbit precesses about the sun. Accounting for the perturbations of the other planets left 43 seconds of arc per century that was previously unexplained by classical physics.

The curvature of spacetime explained by general relativity accounted for the 43 seconds of arc shift in the orbit of Mercury.

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Gravitational Wave Experiments Taylor and Hulse discovered a binary system of two neutron

stars that lose energy due to gravitational waves that agrees with the predictions of general relativity.

LIGO is a large Michelson interferometer device that uses four test masses on two arms of the interferometer. The device will detect changes in length of the arms due to a passing wave.

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NASA and the European Space Agency (ESA) are jointly developing a space-based probe called the Laser Interferometer Space Antenna (LISA) which will measure fluctuations in its triangular shape.

Black Holes

Black Holes are the most profound prediction of general relativity

A black hole is a large body of matter that is so dense that nothing can escape its gravitational attraction, at a given distance, known as the Schwarzschild radius

Black Holes

Do they exist? FOR SURE! Black Holes come in two different sizes: Stellar (5

to 20 solar masses) and supermassive (millions or billions of times the mass of the sun)

Black Holes are detected by either their gravitational influence on nearby bodies or through electromagnetic radiation

Further Implications of GR

Cosmology-the ultimate fate of the universe

The Hawking Effect-the first combination of the quantum theory with general relativity

Conclusion

What have we learned from general relativity? What can we predict using GR? GR is one of the most accurate physical theories

to date

Time travel used to be thought of as just science fiction, but Einstein's general theory of relativity allows for the possibility that we could warp space-time so much that you could go off in a rocket and return before you set out. -(Stephen Hawking)

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Any Questions????????

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Thank You

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