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WARNING: On the original final posted, questions 1 and 5 were the same (I have no idea how that happened as I proofread at least 2 times) but the old quesiton 5 has been removed. There are now 6 questions, and you are to do 5.

The exam will be a 24 hr open book exam starting on
Mon Apr 19 at 8:30 AM PDT (15:30 UTC) and going to 8:30 AM PDT (15:30 UTC) Tues Apr 20.

The finished exam must be sent to me at my email address
unruh@physics.ubc.ca by 8:30 AM Apr 20 PDT
If due to reasons beyond your control, it is impossible to send it to me,
please phone me ( +1 604 7365745 or +1 778 238 7962) to let me know of the
problem before 8:30 Tues.

While it is open book that does not mean that you can consult with, or in any way communicate with any other person
about the exam during that time period. You will be asked to sign a
statement to that effect on the exam. Any such communication is academic misconduct
with all of the consequences attached to such misconduct.

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- Wald-- General Relativity--Probably the best book from the mathematical point of view. He gets things right.
- Misner, Thorne, Wheeler-- Gravitation. Huge and discursive. It covers a lot of material
- Carroll-- Lecture Notes on Relativity -- http://preposterousuniverse.com/grnotes/ Or also in book form Spacetime and Geometry: An Introduction to General Relativity

Here is an extract of a note from the Physics student coordinator:

Ian Cavers (Associate Dean of Science) has already sent more cheating cases from Science to the President's Advisory Committees on Student Discipline (PACSD) than PACSD normally deals with in a full year from the whole university, and he is doing a lot of filtering. So please -

- Talk to your students early in course about cheating - what it is, why they should not do
it, and even though it is easier to do it now, it is easier to catch as all the necessary
evidence is readily available.
- Be explicit and detailed about integrity expectations in your posted course outline and exam
instructions
- Tell students what happens if they are suspected of cheating:
- Interview with instructors and undergraduate chair, and if response is unsatisfactory -
- Zero on course component (e.g. exam) and report sent to Dean's Office, then -
- Interview with the Associate Dean, then -
- At least: Letter of reprimand on permanent file
- More serious cases and all second offences: Move to President's Disciplinary Committee, with consequences up to and including expulsion

- Interview with instructors and undergraduate chair, and if response is unsatisfactory -

- Tell students what happens if they are suspected of cheating:

- Be explicit and detailed about integrity expectations in your posted course outline and exam
instructions

- Nordstrom's theory of gravity
- See Norton for a detailed discussion of the Hole argument (by John Norton, philosopher who is well versed in the mathematics of General Relativity).
- Vectors, Abstract indicees.
- Christophel Symbols Derivation of the covariant derivative by following the more usual procedure of making certain demands on the definition of derivative. This makes it seem far more arbitrary and mysterious than it is.
- Derivation of Parallel transport from metric Note that the "parallalogram" procedure in these notes is slightly different from the one I used in class. In these notes the parallelogram is used to displace the curve through the point at gamma(lambda) defining the vector at lambda, to the a curve through gamma(0) instead of the other way around as in the lecture. This makes no difference to the result.
- Lectures on Lie derivatives.
- Curvature These notes are very similar to what Wald does in his book Ch. 3. The definition of the index order in the curvature tensor is different but due to the symmeteries of the curvature, my tensor is equal to his.
- Linearization of the curvature tensor (altered Feb 27/2019)
- Perihelion advance and Einstein's luck (New versin Mar 12/2019)
- Kennefink's 2009 analysis of the Eddington/Dyson experiment
- Flamm metric Here is also the original paper translated into English
- Schwartzschild solution including Eddington Finkelstein coordinates, and Kruskal
- Paper on the history of the various coordinates for Schwarzschild solution, especially the ones that resolve the horizon "problem".
- Orbits in Schwartzschild including perihelion advance, light deflection, Shapiro time delay, Nordtvedt effect. (Some Misprints corrected and small additions Feb 2021).
- Measurements on the double pulsar
- Lunar Laser ranging experiments and the weight of gravity.
- Gravitational waves solutions Including full non-linear plane wave solution.
- Period evolution of Hulse Taylor Pulsar system showing loss of energy due to grav. radiation.
- Einsten-Rosen paper on
non-linear gravitational waves in Journal Franklin Inst.
223, Pages 43-54 (1937). A previous version of this paper had been
sent to Phys Rev, where the referee HP Robertson had suggested that
the paper was wrong in that it argued that gravitational radiation did
not exist because of the singularity of the solution. Given the first
section
they probably found the Plane wave solutions where the spatial
components of the metric go to zero. They did not recognize that these
were purely coordinate singularities. (That was only done by Bondi,
Pirani and Robinson after the war. See Dan
Kennefink in Physics Today
Physics Today 58, 9, 43 (2005)

Einstein was so upset that the journal had sent his paper to be refereed that he never again published in Phys Rev. - Bondi, Pirani, Robinson paper on plane gravitational waves.
- Talk I gave on Ligo Grav. Wave
detection

PDF

Openoffice ODT

Livingston Gravitational Wave The Livingston gravity wave detector being hit by a gravitational wave with amplitude of about .05 (about 10,000,000,000,000,000,000 times stronger than the one that hit in Sept 2015, the first earth detection of a graviational wave)

- Penrose conformal transformation of the eternal BH spacetime
- Penrose conformal transformation for Vaidya collapse metric.
- ADM formalism for equations
- Papapetrou's paper on deriving geodesic equations from conservation of Energy Momentum tensor. Note that the script T tensor is the tensor density sqrt(|g|) times the energy momentum tensor.
- Geroch and Jang's paper making the previous one a bit more rigorous.
- Dixon extended Papapetrou's treatment to higher moments.
- "Swiss cheese" model for cosmolgy Model in which a spherical void in the dust cosmology is replaced by a Schwartzschild solution with continuity across the boundary. This could also be done for pressure cosmologies, but a shell of pressure (negative surface tension) would be needed to hold back the pressure of the cosmology.
- PhysRevD.14.870 Notes on Black Hole evaporation-- "original" paper with acceleration radiation and expansion on black hole evaporation.
- Fulling ,Ruijsenaars Temperature, periodicity and horizons Proof of periodicity in imaginary time.
- Bogoliubov -- [Corrections Mar 25]paper describing the generic definition of creation and annihilation operators independently of the Hamiltonian. The special case where they are related to the Hamiltonian (Hamiltonian diagonalization) are also described.
- Field Theory The application of the previous work to field theory, and its application to Cosmological particle creation of a scalar field, and the problem with "Hamiltonian diagonalization" as a reasonable definition of "particles."

- Assignment 1 Due Jan 21
- Assignment 2 Due Feb 2
- Assignment 3 Due Feb 16 (Yes, in midterm break, since I want to get out a solution set before the midterm. Don't worry, no lectures in midterm break))
- Assignment 4 Due Thurs Mar15 23:59 PST Added further hints to problems 3 and 4, and extended the time. (Mar 6)
- Assignment 5 Due Tues Apr 6. [Some misprints corrected, and the last sentence completed.]

- Solution 1 with Am J Phys article on Parallax distance
- Solution 2
- Solution 3 (will be released at 23:59, Fri, Feb 19)
- Midterm Solution
- Solution 4
- Solution 5