Bibliotheca Alexandrina Frontiers of Astronomy:
General Relativity Lectures by Prof. Edmund Bertschinger

Updated 3 April 2006

Abstract: These lectures present the essential ideas of general relativity at an advanced undergraduate level and apply them to elementary cosmology and black hole physics. Differential geometry is not used beyond the metric and geodesics; a physical approach based on fields is favored over the geometric viewpoint. The student is assumed to have had upper-level undergraduate courses in classical mechanics, special relativity, and electromagnetism.

Lecture 1: From Special to General Relativity (700 kB Powerpoint)

Lecture 2: Dynamics of Particles, Fluids, and Spacetime (6.7 MB Powerpoint)

Lecture 3: Cosmology in a Robertson-Walker Spacetime (1.8 MB Powerpoint)

Lecture 4: Black Holes (2.25 MB Powerpoint) + (79 kB zip-compressed Java applet)

Lecture Notes 1: Coordinates and Proper Time (useful for Lecture 1, 112kB PDF)

Lecture Notes 2: Gravity, Metrics and Coordinates (useful for Lecture 2, 157kB PDF)

Lecture Notes 3: How Gravitational Forces arise from Curvature (useful for Lectures 1 and 4, 119kB PDF)

Lecture Notes 4: Gravitation in the Weak-Field Limit (useful for Lecture 2, 163kB PDF, more advanced)

Lecture Notes 5: Cosmology (useful for Lecture 3, 526kB)

Undergraduate Assignment 1 (135kB pdf)

Undergraduate Assignment 2 (110kB pdf) and Solution (46kB pdf)

Undergraduate Assignment 3 (136kB pdf) and Solution (71kB pdf)

Undergraduate Assignment 4 (115kB pdf) and Solution (58kB pdf)

Undergraduate Assignment 5 (102kB pdf) and Solution (48kB pdf)

Undergraduate Assignment 6 (90kB pdf) and Solution (45kB pdf)

Undergraduate Assignment 7 (91kB pdf) and Solution (43kB pdf)

Additional materials are available at the MIT OCW Website Physics 8.224: Exploring Black Holes

Recommended textbooks:

Exploring Black Holes by E.F. Taylor and J.A. Wheeler (undergraduate level introduction to GR without tensor calculus)

Gravity: An Introduction to Einstein's General Relativity by J.B. Hartle (advanced undergraduate level, develops tensor calculus as needed)

A First Course in General Relativity by B.F. Schutz (advanced undergraduate level, excellent introduction to tensors and geometric concepts)