PHYS 445-2 General Relativity

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Syllabus:

INSTRUCTOR: Elena Murchikova
CLASSES: Monday/Wednesday 12:30 pm - 1:50pm (Cresge 3-410)
OFFICE: CIERA 7409
OFFICE HOURS: Monday/Wednesdays 11:15 am - 12:15 pm (Tech 123) or by appointment

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'

GRADING:
100% Homework.
All homework submitted on time will receive full grade. Late homework without extension will recieve 50% of the grade. One late homework no questions asked policy.
You must solve all homework problems correctly. If a problem is solved incorrectly, you must redo it the following week. Repeat until it is solved correctly. (If the homework was submitted on time, the final grade after revisions will be 100%.)
At any point, I may ask you to explain how you solved any homework problem in person during office hours.
You can consult your notes and written solutions.
All problem set solutions should be handwritten. Plots can be printed.

Topics:

Lecture 1: Manifolds. Vectors.
Lecture 2: One-forms. Tensors.
Lecture 3: Tensors. q-forms.
Lecture 4: Exterior derivative. Metric tensor.
Lecture 5: Integration of forms. Connection.
Lecture 6: Connection. Christoffel symbols.
Lecture 7: From connection to covariant derivative. Curvature.
Lecture 8: Riemann tensor. Parallel transport.
Lecture 9: Properties of Riemann tensor. Ricci tensor and scalar.
Lecture 10: Physics in curved space. Noether's Theorem.
Lecture 11: Finishing Noether's Theorem. Building General Relativity.
Lecture 12: Einstein's equation.
Lecture 13: Symmetries in GR.
Lecture 14: Schwarzschild metric. Trajectories.
Lecture 15: Falling into black hole.
Lecture 16: Penrose diagrams.
Lecture 17: Basics of Cosmology.
Lecture 18: Small perturbations of the metric.
Lecture 19: Gravitational waves.

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