Relativistic Astrophysics (PHYS*7900)

Code and section: PHYS*7900*01

Term: Fall 2019

Instructor: Daniel Siegel



Daniel Siegel 
Office: MacN 435C 
Extension: 53983

Time and Location

Tuesday, Thursday
8:30a - 9:50a
Mini-Link Room -- MacN 203 (Guelph)
C2 278 (Waterloo) 

Learning Resources 

Required Resources

  • Courselink
    - Course notes
  • Spacetime and Geometry: An introduction to General Relativity
    S. M. Carroll:  (Pearson)
  • General Relativity
    N. Straumann (Springer)

Recommended Resources

  • B. Schutz: A first course in General Relativity (Cambridge)
    (an excellent introduction at the undergraduate level)
  • E. Poisson: Gravity (Cambridge)
  • R. M. Wald: General Relativity (U Chicago Press)
  • C. W. Misner, K. S. Thorne, J. A. Wheeler: Gravitation (Freeman)


30% Assignments
70% Final Exam

Assignments for this course will be handed out and submitted in class. Assignments will not be accepted after the corresponding deadline. Submitted assignment solutions must show calculation details, be legible, and written with a logical flow. Marks on assignments will rapidly approach zero if not presented well. The final exam will be closed text book and closed notebooks.

Course Aims and Objectives 

Course Prerequisites 

We will not have time reviewing standard undergraduate material. In particular, special relativity and associated mathematical methods are a prerequisite (e.g., Chapters 1-4 in Schutz’s book, see above). Students should also review introductory courses on (multi-)linear algebra and be familiar with concepts such as co-vectors and tensors on linear spaces (see, e.g., Chapter 3 in Schutz’s book). Standard undergraduate knowledge of mathematical methods, basic hydrodynamics, and electrodynamics is an expected prerequisite. 

Course Description 

This course provides a graduate-level introduction to General Relativity and its applications to Relativistic Astrophysics. It will introduce the basic mathematical concepts of Lorentzian manifolds, discuss physics in external gravitational fields, and introduce Einstein’s field equations. The theory will be applied to Relativistic Astrophysics and discuss applications such as black hole solutions, neutron stars, and the generation of gravitational waves.

Course Topics 

  • Mathematical foundations: manifolds, vector and tensor fields, Lorentzian manifolds, covariant derivative, geodesics and parallel transport, curvature
  • Equivalence principle and physics in curved spacetime 
  • Einstein’s field equations
  • The Schwarzschild solution and Birkhoff’s theorem
  • Classical tests of general relativity: perihelion advance, deflection of light
  • Neutron stars
  • Generation of gravitational waves

 Assignments and collaboration

Discussion between students regarding assignments is encouraged. All work submitted for grading in this course, however, must be each individual student’s own work. It is not acceptable to share assignment solutions in any way; the assignments are not group projects.

University Statements

Email Communication

As per university regulations, all students are required to check their e-mail account regularly: e-mail is the official route of communication between the University and its students.

When You Cannot Meet a Course Requirement

When you find yourself unable to meet an in-course requirement because of illness or compassionate reasons please advise the course instructor (or designated person, such as a teaching assistant) in writing, with your name, id#, and e-mail contact. The grounds for Academic Consideration are detailed in the Undergraduate Calendar.

Drop Date

Students will have until the last day of classes to drop courses without academic penalty. The deadline to drop two-semester courses will be the last day of classes in the second semester. This applies to all students (undergraduate, graduate and diploma) except for Doctor of Veterinary Medicine and Associate Diploma in Veterinary Technology (conventional and alternative delivery) students. The regulations and procedures for course registration are available in their respective Academic Calendars.

Copies of Out-of-class Assignments

Keep paper and/or other reliable back-up copies of all out-of-class assignments: you may be asked to resubmit work at any time.


The University promotes the full participation of students who experience disabilities in their academic programs. To that end, the provision of academic accommodation is a shared responsibility between the University and the student.

When accommodations are needed, the student is required to first register with Student Accessibility Services (SAS). Documentation to substantiate the existence of a disability is required; however, interim accommodations may be possible while that process is underway.

Accommodations are available for both permanent and temporary disabilities. It should be noted that common illnesses such as a cold or the flu do not constitute a disability.

Use of the SAS Exam Centre requires students to book their exams at least 7 days in advance and not later than the 40th Class Day.

For Guelph students, information can be found on the SAS website.

Academic Integrity

The University of Guelph is committed to upholding the highest standards of academic integrity, and it is the responsibility of all members of the University community-faculty, staff, and students-to be aware of what constitutes academic misconduct and to do as much as possible to prevent academic offences from occurring. University of Guelph students have the responsibility of abiding by the University's policy on academic misconduct regardless of their location of study; faculty, staff, and students have the responsibility of supporting an environment that encourages academic integrity. Students need to remain aware that instructors have access to and the right to use electronic and other means of detection.

Please note: Whether or not a student intended to commit academic misconduct is not relevant for a finding of guilt. Hurried or careless submission of assignments does not excuse students from responsibility for verifying the academic integrity of their work before submitting it. Students who are in any doubt as to whether an action on their part could be construed as an academic offence should consult with a faculty member or faculty advisor.

Recording of Materials

Presentations that are made in relation to course work - including lectures - cannot be recorded or copied without the permission of the presenter, whether the instructor, a student, or guest lecturer. Material recorded with permission is restricted to use for that course unless further permission is granted.


The Academic Calendars are the source of information about the University of Guelph’s procedures, policies, and regulations that apply to undergraduate, graduate, and diploma programs.


Please note:  This is a preliminary web course description. The department reserves the right to change without notice any information in this description.  An official course outline will be distributed in the first class of the semester and/or posted on Courselink.