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.


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

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.