SCHEDULE
MTH 437/537 — Spring 2024


This is a rough schedule from a previous year (with lectures MWF), showing which topic we will cover when.
Most topic links refer to my book on general relativity; others refer to my books on special relativity and differential forms. Each of the links above points to the wiki version of the book, which is not quite the same as the published version.

  Mon Tue Wed Thu Fri
Week 1
(Mar/Apr)
Line Elements
Circle Geometry
Hyperbola Geometry

 
 

Geometry of SR
 

 
 

Physics of SR
 
Week 2
(Apr)

Geodesics
Examples of Geodesics

 
 

Symmetries
Polar & Spherical

 
 

Polar & Spherical
Schwarzschild Metric
Week 3
(Apr)
Physics of GR
Schwarzschild Metric
Properties

 
 

Schwarzschild Geodesics
Schwarzschild Orbits

 
 

Circular Orbits
Null Orbits
Week 4
(Apr)

Radial Geodesics
 

 
 

Rain Coordinates
 

 
 

Observers
Rain Coordinates
Week 5
(Apr/May)
Rindler Geometry
Rindler Geodesics
Extending Rindler

 
 

Extending Schwarzschild
Kruskal Geometry

 
 

Penrose Diagrams
 
Week 6
(May)

Review

 

Midterm

 

Go over midterm
Week 7
(May)

Tidal Forces
Geodesic Deviation

 
 

Geodesic Deviation
Matter, Dust

 
 

Einstein Equation I
Conservation Laws
Week 8
(May)
Einstein Tensor
Einstein Equation II
Cosmological Constant

 
 

Birkhoff's Theorem
 

 
 

Cosmology
Cosmological Principle
Week 9
(May)

Constant Curvature
Robertson–Walker

 
 

The Big Bang
Friedmann Models I, II

 
 
Missing Matter
Standard Models
Cosmological Redshift
Week 10
(Jun)

Memorial Day
 

 
 

Gravitational Waves
 

 
 

Rotating Black Holes