**General Information: Home
About Me CV
Contact /// Physics
Department SUT
Cosmology Group of Sharif
University of Technology **

**Academic Activities:
Research
Interest Publication
Collaborators
My Students Courses
Cosmology Talks درس نامه
ها **

**Other Activities:****
Science Outreach
Outside Physics
Articles
News Press Links
Photo Gallery
فارسی
Հայերէն**

**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: baghram@sharif.edu) ** **

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.

Grading:

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

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:

.....

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.

Assignments:

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

Projects:

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