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General Relativity I  (Spring 2018)

General:  ( This webpage is updated gradually)  - Last Update 20 July 2018

This is a Ph.D. course, which will be held in Physics Department of Sharif University of Technology.

Class Time:  Saturdays and Mondays   15:00 - 17:00

Place: Physics Department - TBA

Office Hours:  Sundays and Tuesdays 9:00 - 10:00  (Or by appointment - Email: baghram@sharif.edu) 

Registered students:  25

About the Course:

About the Course:

The main subject of the course is  a classic course for a Graduate Student to learn about General Relativity.

 The topics that will be covered or touched are as below:

1) A fast review on Special Relativity

2) Manifolds and mathematical foundations of GR

3) Concept of Curvature

4) Einstein Equations

5) The Schwarzschild Solution

6) More about Black Holes

7) GR and Cosmology

8) Perturbation Theory and Gravitation Wave

The main goals of Course:

1) Making a  solid background in GR

2) A preparation for entering the advanced topics in GR.

Teacher Assitants:

Alireza Maleki  ,    Email address   maleki_alireza@physics.sharif.edu   

Grading:

Assignments:    5 points            Please find your grades here

Midterm exam: 3  points          27 Farvardin 1397 / 16 April 2018    Midterm I exam grades are here.

Final Exam:      4  points         9 Tir  1397 / 30 June 2018  @ 15:30  Final exam grades are here.

Take Home:     4  points         Due to Wednesday 20 Tir 1397 /  11 July 2018 till midnight

 Term Paper:    4 points          Due to Wednesday 20 Tir 1397 /  11 July 2018 till midnight

Class Activity:  1 points

Total grade: 21      The Final Results are here!

Suggested Reading:

THE main book of the course is:  Spacetime and Geometry by Sean Carroll - Addison Wesley Publication - 2004

 

Very GOOD  BOOKS ON CHRONOLOGICAL ORDER to keep an EYE on them

1) Gravitation and Cosmology: principles and applications of the general theory of relativity by Steven Weinberg 1972

2) Gravitation - Charles W. Misner, Kip S. Thorne, John Archibald Wheeler  - 1973.

3 ) General Relativity - Robert M. Wald - 1984

4)Introducing Einstein's Relativity by Ray d'Inverno (1992)

5) Exact Solutions of Einstein's field equations- Hans Stephani - 2003

6)General Relativity: An Introduction for Physicists by M. P. Hobson, G. P. Efstathiou, A. N. Lasenby (2006)

7) A first course in General Relativity - Bernard Schutz - 2009

8) Gravitation: Foundations and Frontiers by Thanu Padmanabhan (2010)

 

 

Some  very NICE HISTORICAL BOOKS on story of GR:

1) Subtle Is the Lord: The Science and the Life of Albert Einstein by Abraham Pais (2005)

REVIEW ARTICLES:

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Papers BY THEME:

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Time Line of Lectures:

Lecture  1: ( Saturday  -  3 Feb 2018)

An introduction to the course. Three main ideas of non-Euclidian Geometry - The Physics of Gravity and the Concept of Relativity and the idea of Space-Time is discussed.

Lecture  2: ( Monday  -  5 Feb 2018)

The equivalance principle is described. Then geometrical consequences of this principle is discussed. The vectors and 1-forms are introduced

Lecture  3: ( Saturday  -  10 Feb 2018)

In this lecture we study the concept of  geodesic equation, using the equivalance principle. The concept of Manifold is discussed.

Lecture  4: ( Monday  -  12 Feb 2018)

The geodesic equations are re-studied, we soleve a couple of example ( geometry in 2D sphere and weak field limit). In weak field limit we obtain the Newton's second law for static, weak, non-relativistic regime.

Lecture  5: ( Saturday  -  17 Feb 2018)

In this lecture we define the concept of covariant derivative and intrinsic derivative of geometrical entity.

Lecture  6: ( Monday  -  19 Feb 2018)

In thsi lecture we review the concept of covariant derivative, we solve the geodesic equations for expanding universe and finally we define the Riemann tensor.

Lecture  7: ( Saturday  -  24 Feb 2018)

 

Lecture  8: ( Monday  -  26 Feb  2018)

 

Lecture  9:  ( Saturday  -  3 March  2018)

 

Lecture  10:  ( Monday -  5 March  2018) 

 

Lecture  11:  ( Saturday -  10 March  2018)

In thsi lecture we obtained the geometrical part of the Einstein equation via assumptions of covariant equations - special relativity - conformity and conservation of energy momentum which is the Bianchi identity in geometrical part.

Lecture  12:  ( Monday -  12 March  2018)

In this session we obtain the Einstein equations. The energy momentum tensor is obtained via the variation of the matter action and the concept of Noether current.

Lecture  13:  ( Saturday -  17  March  2018)

We have no class due to Nowrouz 1397.

Lecture  14:  ( Saturday -  7 April  2018)

In this session we discuss the Schwarzschield solution of general relativity, the idea of the singularity and geodesics. We discuss about the killing vectors.

Lecture  15:   ( Monday -  9 April  2018)

In this session we discuss the killing vectors and geodesics of Schwarzschield geometry.

Lecture  16:   ( Monday-  16 April  2018)   27 Farvardin 1397

Midterm Exam

Lecture  17:   ( Saturday -  21 April  2018)

In this lecture, the geodesics equation of Schwarzschiled geometry is discussed.

Lecture  18:   ( Monday -  23 April  2018)

In this session we study the Schwarzschiled Black holes. The coordinate of tortoise, Eddington and Kruskal is discussed

Lecture  19:   ( Saturday -  28 April  2018)

 

Lecture  20:   ( Monday -  30 April  2018)

 

Lecture  21:    ( Saturday -  5 May  2018) 

 

Lecture  22:    ( Monday -  7 May  2018) 

 

Lecture  23:    ( Saturday -  12  May  2018)

 

Lecture  24:    ( Monday -  14  May  2018)

 

Lecture  25:    ( Saturday -  19  May  2018)

 

Lecture  26:    ( Monday -  21  May  2018)

 

Lecture  27:    ( Saturday -  26  May  2018)

 

Lecture  28:    ( Monday -  28  May  2018)

 

Assignments:

1) Problem Set 1 due to Monday 7 Esfand 1396 /  26 February 2018

2) Problem Set 2 due to Monday 20 Farvardin  /   9  April 2018

3) Problem Set 3 due to Monday 27 Farvardin / 16 April 2018

4) Problem Set 4 due to Monday 27 Farvardin / 16 April 2018

5) Problem Set 5 due to Monday 17 Ordibehesht / 7 May 2018

6) Problem Set 6 due to Saturday 9 Tir / 30 June 2018

Term Papers

You can choose one of the projects below for the paper reading, presentation and paper work of this class. 

You can choose your project for term papers  from APS 2015 - General Relativity’s Centennial

Despite tthis projects you can work on

1) Non-Local Gravity.

2) Gravity in higher dimensions.

3) Gravity and condensed matter.

Projects:

Cosmological Constant: 96200333 ,  Cosmic Censorship 96202894,  Information paradox (Arefe Abghari), Gravity in higher dimensions (Ghomi), Inflation )and GR (Ali Hosseinzadeh), Death of stars and Black holes (Mohammad Noormohammadi) 

 

Classic Papers:

 

Useful Links: