Physics 530 Spring 2021
Various details about the course.
Lectures are on Zoom. Contact me for the details.
No assigned text book. There are a number of books which are useful
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.
- 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
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.
Midterm: Feb 23, 2021 1 hour exam Closed book, via Zoom.
Final Exam: To be Scheduled
- Nordstrom's theory of gravity
Norton for a detailed discussion of the Hole argument (by John
Norton, philosopher who is well versed in the mathematics of General
- 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
- Schwartzschild solution including
Eddington Finkelstein coordinates, and Kruskal
- Orbits in Schwartzschild including
perihelion advance, light deflection, Shapiro time delay, Nordtvedt
effect. (Some Misprints corrected and small additions Mar2/19).
- Gravitational waves solutions Including
full non-linear plane wave solution.
- 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.
- Bondi, Pirani, Robinson paper on
plane gravitational waves.
- Talk I gave on Ligo Grav. Wave
- ADM formalism for equations
- Penrose conformal
transformation for Vaidya collapse metric.
- Measurements on the double
- 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
- 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
- Assignment 1 Due Jan 21