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Physics 409: General Relativity

In this webpage, you will find notes and homework solutions for Thomas P. Kling's undergraduate seminar on general relativity.  The notes come directly from a variety of sources, including standard GR texts and the Professor Kling's lecture notes of the graduate relativity course taught by Professor Carlo Rovelli at the University of Pittsburgh in 1997.

Lecture Notes:

Lecture 1: What is Space?
Lecture 1 Supplement: History of the concept of Space
Lecture 2: Special Relativity for Spacetime
Lecture 2 Supplement: Brian Keith thesis
Lecture 3: Equivalence
Lecture 3 Supplement: Brown Astrophysics Journal Club talk on Precision Measurements
Lecture 4: Math 1 - Manifolds
Lecture 5: Math 2 - Vectors
Lecture 6: Math 3 - Dual Vectors
Lecture 7: Math 4 - Tensors
Lecture 8: Math 5 - Metrics
Lecture 8 Supplement: Curvature
Lecture 9: Gravity and Metrics
Lecture 10: Curves
Lecture 10 Supplement: Geodesics
Lecture 11: Coordinates
Lecture 12: Riemann Tensor
Lecture 12 Supplement: Parallel Transport
Lecture 13: General Covariance
Lecture 14: The Einstein Field Equation
Lecture 15: Schwarzschild Space-time and Black Holes 1
Lecture 16: Schwarzschild Space-time and Black Holes 2
Lecture 17: Schwarzschild Space-time and Black Holes 3
Lecture 18: Orbits Near Black Holes
Lecture 19: Hawking Radiation and reading . . . Helfer, Mathur, Smolin, Hsu
Lecture 20: Introduction to Cosmology
Lecture 20 Supplement: Newtonian Cosmology
Lecture 21: Robertson Walker Dynamics
Lecture 22: Big Bang Misconceptions

Homework Assignments:

General Reading Assignment Instructions (follow every time)

Homework 1:  Library and relativity archives
Homework 2:  Time dilation and Length contraction
Homework 3:  Newtonian cosmology
Homework 4:  Properties of Manifolds
Homework 5:  Vectors
Homework 6:  Dual Vectors
Homework 7:  Tensors
Homework 8:  Metrics

Final exam assignment


Homework Solutions:

Homework 2 Solutions
Homework 3 Solutions
Homework 4 Solutions
Homework 5 Solutions
Homework 6 Solutions
Homework 7 Solutions
Homework 8 Solutions

Additional Reading:

Wigner's "Unreasonable effectiveness of mathematics"
NYTimes article: Penrose and Gurzadyan
Martin Gardner on M-Theory and the Weak Anthropic Principle
More famous article -- at least the start of it - will try to distribute entire article

Links for General Relativity:

Los Alamos Archive -- preprint server for physics and astronomy (see gr-qc and astro-ph)
NASA ADS -- preprint server for astronomy
Living Reviews -- requested review articles in GR, solar physics
Gravity book website -- by James Hartle
Topology website -- seems reasonable, haven't fully verified

Other links of interest:

Web-based course on gravitational waves -- by Kip Thorne
Black hole interviews -- site with 10-15 video interviews with prominent people
Baryonic Acoustic Oscillations -- site by D. Eisenstein.
HST Public Site -- for various Hubble related links.
Einstein Exhibit -- American Museum of Natural History Special Exhibit on Einstein.
The time we thought we knew NY Times Op-Ed on January 1, 2004 by Brian Greene.
Black Hole Observations NY Times article on observed tidal effects from black holes.
Profile of Lisa Randall -- NY Times article on the prominent String Theorist
Dangling Particles -- NY Times Op-Ed by Lisa Randall
The Raelians because their funny.