PHYS 445-2 General Relativity

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Syllabus:

INSTRUCTOR: Elena Murchikova
OFFICE: CIERA 7409
OFFICE HOURS: Thursdays 1-2pm (Tech 125)

GRADER: Darsan Bellie

CLASSES: Tuesday/Thursday 2-3:20pm (Annenberg Hall G30)
TEXTBOOKS: Hartle 'Gravity: An Introduction to Einstein's General Relativity'
ALL REFERENCED BOOKS:

Hawking & Ellis 'The Large Scale Structure of Space-Time'
Schutz 'A First Course in General Relativity'
Landau & Lifshitz 'The Classical Theory of Fields. Course of Theoretical Physics Volume 2'
Bogolubov & Shirkov 'Introduction to Theory of Quantized Fields' (for Noether's Theorem)
Misner, Thorne, & Wheeler 'Gravitation'
Meier 'Black hole astrophysics. The engine paradigm'
FINAL EXAM: Take-home

GRADING:
Final letter grades will be assigned based on the total sum of the points acquired during the term. Approximately 55% homework, 40% final exam, and 5% mini-quizzes.

HOMEWORKS and LATE HOMEWORK POLICY:
Problem sets are roughly every two weeks. Due in class on the due date.
Any student can submit one homework up to 1 week late. No questions asked. Please mark this homework as 'Full grade late HW'. Any additional homework submitted 1 day - 1 week late will receive 1/2 of the points. Two weeks late - 1/4 of the points etc.

Unique solutions (i.e. when only one student solves the problem, or when solution provided using different method from everyone else) receive x3 multiplier. If two students submit the same unique solution, they both receive x2 multiplier. If three - x1.5 each. Only correct unique solutions receive the multiplier. If four or more people submit the same solution, it is not considered unique, and no extra points are given. If several solutions to the same problem are submitted, only the highest individual score will be awarded, and not the sum of the scores per each solution.

FINAL EXAM
The Final exam is take-home, closed book, but one page letter-sized handwritten sheet is allowed.
Student(s) who receive significantly higher amount of points (based on the sum of homework and mini-quizzes) than the rest of the class are exempt from taking the Final.

Lecture Content (Books used):

Lecture I: Manifolds. Vectors. Coordinate transformations of vectors. (Hawking & Ellis)
Lecture II: One-forms. Coordinate transformations of 1-forms. Tensors. Coordinate transformations for tensors. (Hawking & Ellis)
Lecture III: Symmetric and anti-symmetric tensors. Vector basis and dual basis of 1-forms. q-forms. Exterior derivative. (Hawking & Ellis)
Lecture IV: Stokes theorem. Metric tensor. Correspondence between vectors and 1-forms. Connection. (Hawking & Ellis, personal notes)
Lecture V: Covariant derivative. Christoffel symbols. (Personal notes, Landau)
Lecture VI: Reminders. Notion of curvature (Schutz)
Lecture VII: Parallel transport. Curvature (Riemann tensor) tensor derivations. (Schutz, Landau)
Lecture VIII: Properties of Riemann tensor. Ricci tensor and Ricci scalar. (Hawking & Ellis, personal notes)
Lecture IX: Noether's theorem. Proof. Stress-energy tensor as a consequence of space-time translational invariance. (Bogolubov & Shirkov)
Lecture X: Einstein's equation. (personal notes, and MTW)
Lecture XI: Weak field Einstein's equation. Newtonian limit. (Schutz)
Lecture XII: Small perturbations of the metric. Gravitational waves. (Personal notes, Landau)
Lecture XIII: Testing GR. Gravitational redshift. Light bending. Shapiro delay. (personal notes)
Lecture XIV: Emission of gravitational waves. LIGO. (personal notes)
Lecture XV: Spherical collapse. Time evolution. (Meier)
Lecture XVI: Hawking radiation.(in-class handout)

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