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General Relativity I (Spring 2017)

General:   (The webpage of the course is updated gradually)  -  Last Update 14 July 2017

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

Class Time:  Saturday and Monday   16:30 -  18:30 

Place:  Physics Department - Class Phys. 3

Office Hours:  Sundays and Tuesdays 9:00 - 10:00  (Or by appointment - Email: 

Number of Registered Students: 18

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 ( I )  (This topic can be touched more in GR II )

7) Perturbation Theory and Gravitation Radiation ( I ) ( This topic can be touched more in GR II )

The main goals of Course:

1) Making a  solid background in GR

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


Assignments:   5 points  

Midterm exam: 4 (3) points     YOU CAN SEE THE RESULTS HERE.      Monday 1 May 2017 / 11 Ordibehesht @  16:30 - 18:30

Final Exam + Take Home: 6 (7) points   YOU CAN SEE THE TAKE HOME EXAM HERE due to Thursday   6 July 2017 / 15 Tir 1396

Class Activity and Term Paper:  5 points     due to Monday   10 July 2017 / 19 Tir 1396

Total grade: 20


You can find your  Mid term grades by clicking here

You can find your  Final Exam grades by clicking here

You can find your  Take Home and Assignments  grades by clicking here

 You can find your  Total  grades

Suggested Reading:

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



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)



Papers BY THEME:


Lectrure Notes and Presentations:

Time Line of Lectures:

Lecture  1: ( Saturday  -  4 Feb 2017)

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  -  6 Feb 2017)

The session will be devoted to Special Relativity, Lorentz transformation and Physics of inertial frames.

Lecture  3: ( Saturday  -  11 Feb 2017)

In this section we study the accelerated observer in special relativity which is a key ingredient to start the general relativity.

Lecture  4: ( Monday  -  13 Feb 2017)

The Physics of the accelerated observers in special relativity is re-studied. Then show how the free-falling observer in a specific coordinate can be studied via Geodesic equation. For this we use the general coordinate transformation technique and we also introduce the concept of metric and affine connections.

Lecture  5: ( Saturday  -  18 Feb 2017)

In this session we will review the geodesic equation and the physics of affine connection and metric. Then we will introduce the vectors and 1-forms as geometrical entities. The concept of Tangent space, dual space, coordinate basis and non-coordinate basis will be discussed.

Lecture  6: ( Monday  -  20 Feb 2017)

In this lecture we will discuss the weak field limit of gravity and geodesics equation. The we will continue our discussion on the concept of vectors and forms.

Lecture  7: ( Saturday  -  25 Feb 2017)

The covariant derivative, and parallel transport is discussed.

Lecture  8: ( Monday  -  27 Feb  2017)

The covariant derivative, and parallel transport is discussed.

Lecture  9:  ( Saturday  -  4 March  2017)

In this lecture we discuss the physics of curvature, Riemann tensor and it's degree of freedom.

Lecture  10:  ( Monday -  6 March  2017) 

In this lecture, we introduce the concept of Energy momentum tensor. The pressureless fluid and ideal fluid is discussed.

Lecture  11:  ( Saturday -  11 March  2017)

In this lecture we study the Einstein field equations.

 Lecture  12:  ( Monday -  3 April  2017)

In this lecture, we will review the path we passed to derive the Einstein equation. Then we discuss the simple solutions of empty space and cosmological constant solution.

Lecture  13:  ( Saturday -  8 April  2017)

The GR-solution for spherical symmetry with a static metric in vacuum, known as Schwarzschild is discussed. The concept of singularity is discussed.

Lecture  14:   ( Monday -  10 April  2017)

The Schwarzschield solution is re-investigated. The physics of spherical symmetric - static space time is discussed.

Lecture  15:   ( Saturday -  15 April  2017)

In this section we start to solve the geodesic equations in Schwarzschild metric. For this task we introduce the Killing vectors.

Lecture  16:   ( Monday -  17 April  2017)

The Schwarzschild Black hole is introduced. The tortoise coordinate and Eddington Finkelstein is discussed.

Lecture  17:   ( Saturday -  22 April  2017)

In this lecture, we will review the concept of the Event Horizon. The causal structure of space time and the extension of Schwarzschild geometry will be studied.

Lecture  18:   ( Monday -  24 April  2017)

The Schwarzschild Black hole is discussed. The concept of conformal (Penrose diagrams) is discussed.

Lecture  19:   ( Saturday -  29 April  2017)

The Conformal diagram is re-studied. The geometry of a star in a static metric is discussed. The Tolman-Oppenheimer-Volkoff equation is introduced.

Lecture  20:    ( Monday -  1 May  2017)  11 Ordibehesht 1396

Midterm Exam

Lecture  21:    ( Saturday -  6 May  2017) 

The no hair theorem is introduced. The concept of static and stationary black holes is introduced.

Lecture  22:    ( Monday -  8  May  2017)

In this lecture the  Reissner–Nordström black holes is studied.

Lecture  23:    ( Saturday -  13  May  2017)

The Kerr Black hole is discussed. The concept of ergosphere and killing horizon is studied.

Lecture  24:    ( Monday -  15  May  2017)

The thermodynamic of Black Holes is discussed by using Penrose processes in Kerr Black holes.

Lecture  25:    ( Saturday -  20  May  2017)

In this lecture we introduce the idea of  surface gravity and its conection with killing horizons is discussed. We start the idea of perturbation theory in GR.

Lecture  26:    ( Monday -  22  May  2017)

Gravitational Wave I

Lecture  27:    ( Saturday -  27  May  2017)

Gravitational Wave II

Lecture  28:    ( Monday -  29  May  2017)

In this lecture, we watch a documentary of through wormholes - Black Holes and we discuss and finalize the course.


1) Problem Set 1  due to Sat   4 March 2017 / 14 Esfand 1395

2) Problem Set 2  due to Sat  11 March 2017 / 21 Esfand 1395

3) Problem Set 3  due to Sat   8  April 2017  /  19 Farvardin 1396

4) Problem Set 4  due to Sat  15 April 2017 / 26 Farvardin 1396

5) Problem Set 5:  The midterm exam!  due to 21 June 2017 31 Khordad 1396

6) Problem Set 6  due to 21 June 2017 31 Khordad 1396


You can choose one of the projects below for the paper reading, presentation and paper work of this class. The projects are going under an intensive update by adding references and review articles and key papers about them.

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