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P415 General Relativity & Cosmology

Instructor:
Office: Elliott 118
Office hours: Mondays 2:30-3:30pm
Email: aritz@uvic.ca
Lectures: 1:00-2:30pm, Mon & Thurs 
Prerequisites: PHYS 321A, PHYS 326, MATH 346


This is a 4th year course introducing Einstein's general relativistic theory of gravity, and 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.

Territory Acknowledgement: We acknowledge and respect the Lək̓ʷəŋən (Songhees and Esquimalt) Peoples on whose territory the university stands, and the Lək̓ʷəŋən and W̱SÁNEĆ Peoples whose historical relationships with the land continue to this day.


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

The course will be assessed according to the following three components:

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

There will be 5 assignments during the semester, and you will generally have ~1.5 weeks to complete each of them. The cumulative assignment grade will be computed from the top 4, with the lowest grade discarded. Assignments form an integral part of the course, used to expand on the material in the lectures in various ways. Investing time in them is beneficial for understanding the novel concepts involved in the theory of general relativity, and a key to success in this course.

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, percentages will be assigned which are consistent with them.

Note on the use of calculators in exams: Calculators are not really required for this course, but a reminder about the general university policy; "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."

After completing the course, you will:

  • have detailed knowledge of how special relativity imposes a causal structure on events in space and time, and the associated Minkowski spacetime geometry.
  • be able to explain how the equivalence principle leads to a geometric description of gravity, in the form of Einstein's general theory of gravity.
  • have detailed knowledge of how space and time are curved around spherically symmetric mass distributions, you can solve practical orbit and trajectory problems in such spacetime geometries, and you know the basic properties of Schwarzschild black holes.
  • have acquired basic knowledge of the cosmological concordance model, and how it is based on Einstein's theory of gravity.
  • be able to communicate basic principles and complex topics in GR in a clear and pedagogical way.