General Relativity and Cosmology

This is the home page for the course, PH587 General Relativity and Cosmology, that I will be teaching during Spring 2009 (Jan.-Apr. 2009) at the Indian Institute of Technology Madras. It is being offered for the first time by the Physics Department at IITM (There used to be a course titled Geometry of Space and Cosmology that was offered by the maths department during the 80s, so one cannot truly claim that GR is being offered for the first time at IITM.).

($\longleftarrow$ Formation of a black hole due to collapsing matter — picture produced by G. 't Hooft and reproduced without his permission! I hope he doesn't mind. )

## Target Audience

It is an elective course in the M.Sc. as well as B.Tech. (Engg. Physics) curriculum. I also expect Physics minors to do this course.

## Pre-requisites

A key pre-requisite for this course is an open mind! It is useful to know the special theory of relativity (words like Inertial_frames, Lorentz_transformations, Four-vectors etc. should make sense).
Einstein's 1905 paper, On the electrodynamics of moving bodies (English translation), is also an interesting read. I have added a pdf file of some material (on SR) that we used to hand out to Physics II students towards the end of the course.

## Assessment

 Assignments 10% Two Quizzes 2$\times$20% Final 50%

## Course Notes

I plan to include notes (or links to notes by others) on various topics that are discussed in the class lectures.

Geodesics on the two-sphere

Sean Carroll put his Lecture Notes on General Relativity on the arXiv. You may find it useful for this course — these lectures eventually became the book listed below in the references.

## Online Resources

General Relativity Today (circa 2007) — a nice overview given by Thibault Damour
Tests of General Relativity:
Historical Description of the precession of Mercury by C. Myles of Texas Tech
Gravity Probe B: Testing Einstein's Universe
Gravitational Waves:
LIGO (Light Interferometer Gravitational-wave Observatory)
Hulse and Taylor -- 1993 Nobel Prize Press Release, A nice technical review (written in 1995) on the Hulse and Taylor work by C. Sivaram of the Indian Institute of Astrophysics
Cosmology:
Ned Wright's Cosmology Tutorial
Dark Energy
WMAP has a nice summary on Cosmology (worth reading)

## Official Course Content

Prelude to general relativity: Review of Special Relativity(SR); global inertial frames; four-vectors and tensors in SR; covariance of equations under Lorentz transformations.

General relativity: Symmetries and Conservation laws, General coordinate invariance, Principle of Equivalence. Tensors in curved spacetime, Connection, Parallel transport, Covariant Derivative, Bianchi identities. Metric, Energy-momentum and Curvature tensors. Geodesics. Einstein’s equations, Simple solutions.

The predictions of general relativity: Precession of the Planetary Orbits, The Gravitational Red shift, Gravitational waves and their signatures, Bending of Light. Black holes. Singularities, General properties of Black holes and Black hole Thermodynamics.

Cosmology: Homogeneity and Isotropy. Friedmann-Robertson-Walker metric. Standard Model of Cosmology. Elementary ideas on Big Bang Nucleosynthesis, Phase Transitions, Structure Formation. CMBR Anisotropy.

## Textbooks

1. J.B. Hartle, Gravity: An introduction to Einstein's General Relativity, Pearson Education (2003).
2. B. Schutz, A first course in General Relativity, Cambridge University Press(1985).

## References

1. S. Weinberg, Gravitation and Cosmology, John Wiley & Sons (1972).
2. C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, W. H. Freeman and Company (1973).
3. R. M. Wald, General Relativity, Overseas Press (India) Private Limited (1984).
4. S. Carroll, Spacetime and Geometry: An Introduction to General Relativity, Benjamin Cummings (2003)
5. S.Weinberg, The First Three Minutes: A modern view of the origin of the Universe, Basic Books (1993).
6. Simon Singh, Big Bang: The Origin of the Universe, Fourth Estate (2005).