P415 General Relativity & Cosmology

Instructor: Adam Ritz
Office: Elliott 103
Office hours: Mondays 2:30-3:30pm
Email: aritz@uvic.ca
Lectures: 1:00-2:30pm, Mon & Thurs in Elliott 161 

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
  • Black Holes
  • Cosmology

See the course syllabus for further details.

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
    • (Extra topics)*: Gravitational waves,...
  • Black Holes [Ch. 12,13]
    • Orbits, coordinate systems
    • astrophysical evidence
  • Cosmology [Ch. 17,18]
    • Homogeneous, isotropic spacetimes
    • FRW metrics, and the thermal history
    • (Extra Topics)*: Inflation, structure formation,...
*Covered if time permits
Further online material for the course, including:
  • course notes
  • assignment sheets
  • sample solutions

will be available at the PHYS 415 course page in CourseSpaces
The course will assessed according to the following three components:
  • Assignments: 25%
  • Mid-term: 25%
  • Final exam: 50%

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 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

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.