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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
Oral Exam: 3 points See final Results
Final Exam: 3 points YOU CAN SEE THE RESULTS HERE
Take Home: 3 points See final Results
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:
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Papers BY THEME:
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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