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General Relativity I  (Spring 2021)


General:  ( This webpage is updated gradually)  - Last Update 20 July 2021

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

Class Time:  Saturdays and Mondays   17:30-17:30

Place: https://vc.sharif.edu/ch/baghram

Office Hours:   by appointment - Email: baghram@sharif.edu 

Registered students: 


About the Course:

About the Course:

This is a classic course for a Graduate Student to learn about the fascinatin theory of 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:

Mr. Arad Nasiri             Email address:  aradn1997@gmail.com

 

 


Grading:

Assignments:             4 points            YOU CAN SEE THE RESULTS HERE

Midterm Exam:         3  points           YOU CAN SEE THE RESULTS HERE  / Monday 13 Ordibehesht 1400 - 3 May 2021

NOTE ON MIDTERM EXAM

 MID TERM I

GR IMPORTANT FINAL NOTE

Oral Exam:               3  points            See final Results

Final Exam:              3  points            YOU CAN SEE THE RESULTS HERE

FINAL EXAXM

Take Home:             3  points            See final Results

TAKE HOME

Term Paper:             3 points           See final Results

Class Activity:           1 point

Total grade: 20      YOU CAN SEE THE RESULTS 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)

9) Nonlocal Gravity by Bahram Mashhoon (2017)

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:

.....

Papers BY THEME:

....


Lectrure Notes and Presentations:

GR- Lecture Note - Review of Special Relativity

GR- Lecture Note - From Locality to Geodesics equation

GR- Lecture Note - Vectors on Manifolds

GR- Lecture Note - Forms and Derivatives

GR-Lecture Note - Covariant Derivative

GR-Lecture Note - Parallel Transport

GR-Lecture Note - Accelerated Observers and degrees of freedom

GR- Leccture Note - Manifolds I

GR- Lecture Note - Manifolds II

GR- Lecture Note - diffeomorphism

GR Lecture Note - Forms and Exterior Derivatives

GR- Lecture Note - Riemann Curvature tensor

GR- Lecture Note - Energy Momentum Tensor

GR- Lecture Note - Einstein field Equations

GR- Lecture Note - Einstein - Hilbert action

GR- Lecture Note -Cosmological Constant I

GR- Lecture Note -Cosmological Constant II

GR-Lecture Note- Schwarzschild I

GR-Lecture Note- Schwarzschild II

GR-Lecture Note- Schwarzschild III

GR-Lecture Note - Schwarzschild Black Hole I

GR-Lecture Note - Schwarzschild Black Hole II

GR-Lecture Note- Conformal Diagrams

GR-Lecture Note - Black Hole and stars

 


Time Line of Lectures:

Lecture  1: ( Saturday  - 25  Bahman 1399 -  13 Feb 2021)

A Historical back ground of the concepts of Gravity - SpaceTime and Geometry.

Lecture  2: ( Monday  -  27 Bahman 1390 -  15 Feb 2021)

A review of  Special Relativity

 Lecture  3: ( Saturday  - 2 Esfand  1399 -  20 Feb 2021)

From Locality to geodesic equation  

* WE WILL NOT HAVE A LECTURE ON MONDAY 4 Esfand 1399/ 22 Feb 2021

due to TEHRAN MEETING on The Cosmology at the crossroads

 Lecture  4: ( Saturday  - 9 Esfand  1399 -  27 Feb 2021)

Afine Connection, metric tensor, weak field limit of geodesic equation, gravitational redshift

 Lecture  5: ( Monday  - 11 Esfand  1399 -  1 March 2021)

Tensor calculus, Manifolds and tangent space, directional derivatives - I

Lecture  6: ( Saturday  - 16 Esfand  1399 -  6 March 2021)

Tensor calculus, Manifolds and tangent space, directional derivatives - II

Lecture  7: ( Monday - 18 Esfand  1399 -  8 March 2021)

Derivatives and forms in GR I

Lecture  8: ( Saturday - 23 Esfand  1399 -  13 March 2021)

Derivatives and forms in GR II

Lecture  9: ( Monday - 25 Esfand  1399 -  15 March 2021)

Riemann Tensor, Ricci tensor, Einstein tensor and Ricci scalar.

Lecture  10: ( Saturday - 14 Farvardin 1400 -  3 April 2021)

Einstein field equations.

Lecture  11: ( Monday - 16 Farvardin 1400 -  5 April 2021)

FRW cosmology as an example of Einstein field equations.

Lecture  12: ( Saturday- 21 Farvardin 1400 -  10 April 2021)

FRW cosmology and Cosmological constant problem I

Lecture  13: ( Monday- 23 Farvardin 1400 -  12 April 2021)

FRW cosmology and Cosmological constant problem II

Lecture  14: ( Monday- 28 Farvardin 1400 -  17 April 2021)

Schwarzschield Solution I

Lecture  15: ( Monday- 30 Farvardin 1400 -  19 April 2021)

Schwarzschield Solution II

 

 


Assignments:

Please send your homeworks to sh.baghram@gmail.com (pdf file - scanned)

You have the opportunity to use 7 days in total to send homeworks after deadlines.

1) The Problem Set 1       Look at Lecture Note  GR- Lecture Note - From Locality to Geodesics equation

       Due to Monday 11 Esfand 1399 /   1 March 2021  till 23:59  

2) The Problem Set 2       Due to Friday 22 Esfand 1399 /   12 March 2021  till 23:59 

3) The Problem Set 3       Due to Friday 20 Farvardin 1400 /    9 April 2021  till 23:59 

4) The Problem Set 4       Due to Friday 20 Farvardin 1400 /    9 April 2021  till 23:59 

5) The Problem Set 5       Due to Friday 27 Farvardin 1400 /    16 April 2021  till 23:59 

6) The Problem Set 6       Due to Friday 27 Farvardin 1400 /    16 April 2021  till 23:59  

7) The Problem Set 7       Due to Friday  10 Ordibehesht 1400 /   30 April 2021  till 23:59   

8) The Problem Set 8       Due to Friday  14 Khordad 1400 /    4 June 2021  till 23:59 

       

 


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:

 

 


Classic Papers:

 


Useful Links:

Gravitationa lensing Lecture   by Jonathan Pritchard - Harvard

Gravitationa lensing Lecture   by Nastassia Grimm Zurich

Gravitatioan Lensing  by Massimo Meneghetti Heidelberg

Gravitatioan Lensing  by Martin Kilbinger IAP