Readings

Required Text

Amazon logo Carroll, Sean. An Introduction to General Relativity: Spacetime and Geometry. San Francisco, CA: Addison Wesley, 2003. ISBN: 9780805387322.

Other Relevant Texts

Amazon logo Misner, Charles W., Kip S. Thorne, and John Archibald Wheeler. Gravitation. San Francisco, CA: W.H. Freeman, 1973. ISBN: 9780716703440.

Amazon logo Schutz, Bernard. A First Course in General Relativity. New York, NY: Cambridge University Press, 1985. ISBN: 9780521277037.

Amazon logo Hartle, James. Gravity: An introduction to Einstein's general relativity. San Francisco, CA: Addison-Wesley, 2002. ISBN: 9780805386622.

Amazon logo Weinberg, Steven. Gravitation and Cosmology. New York, NY: Wiley, 1972. ISBN: 9780471925675.

Amazon logo Wald, Robert. General relativity. Chicago, IL: University of Chicago Press, 1984. ISBN: 9780226870335.

Amazon logo Poisson, Eric. A Relativist's Toolkit. New York, NY: Cambridge University Press, 2004. ISBN: 9780521830911.

WEEK # TOPICS READINGS
1

Geometric Viewpoint on Physics in Flat Spacetime: Vectors and Dual Vectors, Tensors

Special Relativity

Carroll. Chapter 1.
This chapter gets into topics we will cover in Week #2.

Schutz. Chapters 2 and 3.
This also covers topics we will save for Week #2.
Schutz, Chapter 1 is good if you would like to review Special Relativity.

2

Geometric Viewpoint on Physics in Flat Spacetime: Energy and Momentum, Conserved Currents, Stress Energy Tensor

Transformation Law for Tensors

Carroll. Chapter 2.
Carroll gets into quite a bit more technical detail than I would like to cover. In particular, the details of manifold mathematics are beyond the scope of what we intend to cover. The remainder of the chapter is quite useful for us (though again a bit more formal than my preferred approach).

Schutz. Chapters 3 and 4.

3

Metric in a Curved Space

Orthonormal and Coordinate Bases; Derivatives; Tensor Densities; Differential Forms and Integration

Gauge/Coordinate Transformations

Schutz. Chapter 5.
4

Metric in a Curved Space (cont.)

Orthonormal and Coordinate Bases; Derivatives; Tensor Densities; Differential Forms and Integration (cont.)

Gauge/Coordinate Transformations (cont.)

Carroll. Chapter 3, especially sections 3.1-3.5. (We may begin discussing Curvature Tensors this week, in which case section 3.6 and onward is also relevant.)

Schutz. Chapter 6, especially sections 6.1-6.4. (If we get to Curvature Tensors this week, section 6.5 and onward is also relevant.)

5

Connection and Curvature, Geodesics

Introduction to Curvature

Last week's readings are still relevant for this week.

6

Curvature Continued: Geodesic Deviation, Bianchi Identity

Killing Vectors and Symmetries

Carroll. Sections 3.6-3.10.
Section 3.9 can be omitted; it covers a topic that is interesting, but not strictly necessary for our development. Also, I find section 3.10 to be somewhat unsatisfying; please read it, but be aware that I will develop Geodesic Deviation somewhat differently.

Schutz. Sections 6.5 and 6.6 are good supplemental readings; Schutz develops Curvature Tensors in a somewhat more straightforward (and to my mind physical) way than Carroll does. There is a bit of hand-waving in places, though, which I hope to reduce when I develop these quantities in lecture.

7

Einstein's Equation and Gravitation

Cosmological Constant

Hilbert Action

Carroll. Chapter 4.
Section 4.6 is not necessary for 8.962, but is interesting stuff and definitely worth reading. Section 4.8 does not have to be examined too closely, but is also worth reading (at least cursorily). Note: Section 4.8 makes it clear why Carroll's stuff typically includes "Torsion Terms"; I've been strictly ignoring them since Torsion does not fall under the scope of General Relativity.
8

Weak Field/Linearized General Relativity

Gauge Invariant Characterization of Gravitational Degrees of Freedom

Spacetime of an Isolated Weakly Gravitating Body

Carroll. Sections 7.1-7.4.
Note: the post-Spring Break material will focus on applications of General Relativity, with a particular emphasis on Astrophysical Problems. As such, we are going to jump around in Carroll a bit.
9 Gravitational Waves

Carroll. Sections 7.5-7.7.

The Basics of Gravitational-wave Theory, by Flanagan and Hughes (optional).

10 Gravitational Lensing

I don't have very good suggestions for reading this week. Our discussion of Gravitational Lensing is going to be quite basic; probably the discussion in Hartle's textbook is relevant.

Carroll gives somewhat more advanced discussion in the chapter on Cosmology (section 8.6); I highly recommend that section after we have discussed Cosmology in class.

The OCW notes by Bertschinger and Barkana motivate the starting point of gravitational lensing far more rigorously than I will do in lecture; these notes are highly recommended to students who are interested in a deeper discussion of this subject. (PDF)

11

Cosmology

Friedmann-Robertson-Walker Solution; Distance Measures and Redshift

Our Universe

Carroll. Chapter 8.
This is my favorite chapter in this textbook - Sean really earns his royalty checks here.
12

Schwarzschild Solution

Birkhoff's Theorem, Metric of a Spherical "Star"

Carroll. Sections 5.1 - 5.5

Misner, Tayler and Wheeler. Sections 23.1 - 23.7

13

Black Holes

Collapse to Black Hole; Orbits of a Black Hole

Kerr and Reissner-Nordstrom Solutions

Carroll. Section 5.6 - 5.8 and Chapter 6.  

Misner, Tayler and Wheeler. Chapters 32 and 33.

14 Advanced Topics and Current Research in General Relativity

Luc Blanchet, "Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries", Living Rev. Relativity v9, 4 (2006).

Luciano Rezzolla, "Gravitational Waves from Perturbed Black Holes and Relativistic Stars," Lectures given at the Summer School on Astroparticle Physics and Cosmology, ICTP, July 2002.