General Relativity , PHYS 324 00
SYLLABUS, Spring 2020
Instructor: Alexios Polychronakos, Somewhere in Spacetime
Textbook: A first course in general relativity, Bernard F. Schutz, Cambridge University Press, plus additional occasional class notes.
Structure of Lectures: This course will be conducted fully remotely, using Zoom. Please make sure you have the necessary technological resources.
Office hours: by appointment (email me for a Zoom, Skype or phone meeting).
Communication: Class material will be distributed via Blackboard and Cunyfirst. Messages will be sent through the Cunyfirst system to all officially enrolled students.
I regret that I will not operate within social media platforms (Facebook, Twitter, Quack etc.)
Topics covered: The course will cover part of the material in Schutz’s book plus additional special topics and recent advances. Topics includes: Review of special relativity; spacetime and Minkowski metric; 4-vectors and 4-tensors; stress-energy-momentum tensor; curved manifolds: generalized coordinates, metric, connection, curvature; physics in a curved spacetime manifold: geodesic motion, small curvature, relation to motion in Newtonian gravity; Einstein’s equations; Newtonian limit; gravitational waves; vacuum spherical solutions: equatorial motion, precession of perihelium, bending of light; black holes: horizons and singularities; elements of cosmology.
Structure of course: Lectures will cover theory, work out examples and solve problems as needed. There will be no strict separation between “lecture” and “recitation” sessions. You should attend lectures, solve problems as suggested in class, do the assigned homework and review the necessary material from the book or your notes. This is a hard course that requires your full attention and diligence. Here is some common sense advice, in the first person, which you may disregard at your own peril:
• Do not fall behind! General Relativity is unforgiving to those who do not take it seriously, and cannot be “crammed” in a hurry.
• Ask questions! Ask me during class if anything is unclear, or whenever you have an idea or doubt. The only bad question is the one not asked!
• Solve problems! Reading and fully understanding the material, but not solving enough problems, is making no progress at all. Solve the examples given in class or the textbook and the assigned homework problems, as well as extra problems on your own.
• If you have serious difficulties or problems arrange to see me! Do this earlier rather than later. You cannot afford to stay paralyzed and wait until it is too late for help. Again, this is a course for committed aficionados, not intellectual tourists.
Again, don’t let the word “Introduction” in the title of the course fool you. This is a hard course addressed to devoted and committed aficionados of the material, not intellectual tourists. Come in full fighting gear or stay out!
Attendance, Homework: You are strongly advised to attend all lectures. There will be assigned homework that will earn you 15% credit for the course.
Educational Objectives: Upon finishing this course you should
-Have a good knowledge of Special Relativity, spacetime concepts, 4-vectors and 4-tensors
-Be able to solve problems of particle motion in Minskowski spacetimes
-Master the basic mathematics of curved manifolds and their metric, connection and curvature
-Understand geodesics and geodesic motion in curved spacetime
-Understand the basic structure of Einstein’s equations and their Newtonian limit
-Understand the basic physics of gravitational waves
-Understand the Schwarzschild metric, black holes and their gravitational effects
-Have a basic qualitative knowledge of cosmology
Behavior and Cheating: You are expected to act responsibly and follow the rules of the course and of civility. This includes not talking or funneling in noises from your environment, engaging in extracurricular activities during lectures, and addressing the lecturer and your fellow students politely. You can have food, quietly, but I discourage alcohol and encourage caffeinated drinks!
Cheating during exams, homework or any other circumstance is grounds for failing the course and suffering severe academic consequences.
Exams: One Midterm exam and one comprehensive Final.
Exam Structure: Exams are open book: you are permitted to use your books, notes, or any passive device you wish. Communication during the exam is strictly forbidden: no talking, laptops, phones (smart or otherwise), other wireless devices, and interactions with any sentient beings.
Exams will be conducted via Zoom. A camera showing clearly your face and your workspace is required. For clarifications on what is being asked use the "raise your hand" feature.
An oral follow-up of any exam can be requested of any student without cause.
Missing an Exam: For absence due to serious and fully documented medical or family emergency an equally hard make-up exam will be given. It is to your advantage to be there for the scheduled exam.
Special Circumstances: Students who qualify for extra time, a quiet test environment or other special accommodations due to a documented condition should present evidence and notify me at the beginning of the course, and should make appropriate arrangements with the AccessAbility office. Students with religious or other restrictions on the dates they can take exams should communicate them to me at the beginning of the course. Every effort will be made to accommodate them, within the constraints of the schedule and other students’ needs and limitations.
Etiquette: Joint on time for the exam. Have your full testing environment ready and conforming to the stated rules. Please take care of your physical needs beforehand. Emergency bathroom visits or other brief absences will automatically trigger an oral follow-up of the exam.
Grades: Your letter grade will be based on a numerical score to be computed as follows:
Homework 15%, Midterm 35%, Final 50%. No single exam will guarantee your passing the course.
I reserve the right to change the details of this syllabus during the semester.