PHYS 415 - University of Victoria

P415 General Relativity & Cosmology

Instructor: Adam Ritz
Office: Elliott 118
Office hours: Mondays 2:30-3:30pm
Email: aritz@uvic.ca
Lectures: 1:00-2:30pm, Mon & Thurs in CLE A312

This is a 4th year course on the general relativistic theory of gravity, covering the following broad areas:

Special relativity and spacetime
Equivalence principle and gravity as geometry
Curved spacetime geometry, geodesics, curvature
Einstein's equations, the Schwarzschild geometry, and solar system tests
Applications: Black Holes, Gravitational waves, Cosmology

See the course syllabus for further details.

Syllabus
Recommended Texts
Notes and Assignments
Assessment

This is a 4th year course on general relativity, and (time permitting) will cover the following topics. The chapter references refer to the text by Hartle.

Overview
- Introduction, review of Newtonian gravity and Galilean relativity
Special Relativity and Spacetime [Ch. 4,5]
- Lorentz transformations and 4-vectors
- Energy-momentum and its conservation
- Lagrangian for a probe particle
Equivalence Principle and Gravity as Geometry [Ch. 6,7,8]
- Inertial and gravitational mass
- The equivalence principle; Pound-Rebka experiment
- gravity as geometry, geodesic motion
- Newtonian gravity in geometric form, post-Newtonian corrections
Spacetime Geometry and Einstein's Equations [Ch. 9,10 (plus 20,21,22 which are more advanced)]
- Tensors and general covariance
- Covariant derivatives, curvature
- Einsteins equations
- Schwarzschild solution
- Solar system tests

Applications
- Black holes [Ch. 12,13]
  - Orbits, cooridnate systems
  - Astrophysical evidence
- Gravitaitonal Radiation [Ch. 16]
  - Wave solutions
  - Polarization
- Cosmology [Ch. 17,18]
  - Homogeneous, isotropic spacetimes
  - FRW metric, thermal history
  - Lambda CDM cosmology

The (optional) course text is:

Gravity: An Introduction to Einstein's General Relativity, J.B. Hartle

This is an excellent introductory text from one of the well-known names in the subject. Hartle takes a very physical approach, adding new mathematical content only when required, and incorporating many up-to-date applications and examples. Although we will not always follow the same order of topics, this text would make a very useful complementary source to the lectures.

There are of course many (many!) other texts which introduce general relativity. Most follow a slightly more mathematical route than Hartle. Some good course texts which are at a similar or somewhat higher level than this course include:

A First Course in General Relativity, B.F. Schutz
General Relativity, I.R. Kenyon
Spacetime and Geometry: An Introduction to General Relativity, S.M. Carroll

For more advanced material (generally well above the level of this course), standard references are:

Gravitation and Cosmology , S.W. Weinberg
General Relativity, R.M. Wald

Further online material for the course, including:

course notes
assignment sheets
sample solutions

will be available at the PHYS 415 course page in Brightspace

The course will assessed according to the following three components:

Assignments: 35%
Mid-term quiz: 25%
Final exam: 40%

There will be 5 or 6 assignments during the semester, and you will generally have between ~1.5 weeks to complete each of them. They form an integral part of the course, used to expand on the material in the lectures in various ways.

Dates for the mid-term quiz and final exam are TBA.

The final grade will follow the University's percentage grading scheme, with the following universal conversion between letter and percentage grades:

A+ (90-100)
A (85-89)
A- (80-84)
B+ (77-79)
B (73-76)
B- (70-72)
C+ (65-69)
C (60-64)
D (50-59)
E (TBD)
F (0-49)

If the application of this scheme would result in grades deemed by the instructor to be inconsistent with the University's grading descriptions (which can also be found on p.64 of the current University Calendar), percentages will be assigned which are consistent with them.

NB: Use of calculators in exams (NB: not really required for this course)

On all examinations the only acceptable calculator is the Sharp EL-510R. This calculator can be bought in the Bookstore for about $10. DO NOT bring any other calculator to the examinations.