Geometric Viewpoint on Physics in Flat Spacetime: Vectors and Dual Vectors, Tensors
Carroll. Chapter 1.
Schutz. Chapters 2 and 3.
Geometric Viewpoint on Physics in Flat Spacetime: Energy and Momentum, Conserved Currents, Stress Energy Tensor
Transformation Law for Tensors
Carroll. Chapter 2.
Schutz. Chapters 3 and 4.
Metric in a Curved Space
Orthonormal and Coordinate Bases; Derivatives; Tensor Densities; Differential Forms and Integration
|Schutz. Chapter 5.|
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.)
Connection and Curvature, Geodesics
Introduction to Curvature
Last week's readings are still relevant for this week.
Curvature Continued: Geodesic Deviation, Bianchi Identity
Killing Vectors and Symmetries
Carroll. Sections 3.6-3.10.
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.
Einstein's Equation and Gravitation
|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.
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)
Friedmann-Robertson-Walker Solution; Distance Measures and Redshift
|Carroll. Chapter 8. |
This is my favorite chapter in this textbook - Sean really earns his royalty checks here.
Birkhoff's Theorem, Metric of a Spherical "Star"
Carroll. Sections 5.1 - 5.5
Misner, Tayler and Wheeler. Sections 23.1 - 23.7
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|| |
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.