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
firstname.lastname@example.org 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.
No assigned text book. There are a number of books which are useful
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 --
Or also in book form Spacetime and Geometry: An Introduction to
There are a number of other books available as well.
I will also upon occasion put up some lecture notes, Assignments,
My office is Henn 311 (inside to table and turn right) The return assignment
tray is beside the door.
Phone: (604) 822 3853
Course: This will cover the field of gravity or General Relativity. I intend
to cover gravity waves fairly extensively, but will also cover Tensor
analysis, Black hole solutions, and quantum effects around black holes.
There will be assignments in the course worth from 20-25% of the grade, an
essay due on the last day of class (worth 30-35%) and a final exam worth the
rest of the marks.
Statement re remote learning
During this pandemic, the shift to online learning has greatly altered teaching and studying at UBC,
including changes to health and safety considerations. Keep in mind that some UBC courses might cover
topics that are censored or considered illegal by non-Canadian governments. This may include, but is not
limited to, human rights, representative government, defamation, obscenity, gender or sexuality, and
historical or current geopolitical controversies. If you are a student living abroad, you will be subject to the
laws of your local jurisdiction, and your local authorities might limit your access to course material or take
punitive action against you. UBC is strongly committed to academic freedom, but has no control over
foreign authorities (please visit http://www.calendar.ubc.ca/vancouver/index.cfm?tree=3,33,86,0 for an
articulation of the values of the University conveyed in the Senate Statement on Academic Freedom).
Thus, we recognize that students will have legitimate reason to exercise caution in studying certain
subjects. If you have concerns regarding your personal situation, consider postponing taking a course
with manifest risks, until you are back on campus or reach out to your academic advisor to find substitute
courses. For further information and support, please visit: http://academic.ubc.ca/support-
Plagerism, cheating, etc
In one word
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
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
There is apparently a UBC graduate STudent chat channel where you can drop in
to talk with other grad students.
I have no idea how this works, but it may offer a place where you can meet up
with other students taking this course to discuss problem, assignments,
confusions, etc. I have no used it so cannot offer any advice. If anyone wants
to give more information, pls email me, and I can post it here.
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.
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.
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
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.
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)
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.
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
Assignments and solutions are in pdf form. You can read them with acroread
from Adobe, or many other readers (eg on Linux, xpdf, Okular, gv are ones I