PHYS 445-2 General Relativity

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Syllabus:

INSTRUCTOR: Elena Murchikova
OFFICE: CIERA 7409
OFFICE HOURS: Wednesdays 11:30-12:30 (Tech 123)

CLASSES: Monday/Wednesday 12:30-1:50pm (Tech L168)
TEXTBOOKS: Schutz 'A First Course in 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:
Approximately 75% homework, 25% oral exam on theory.

Topics (Books used):

Topic I: Manifolds. Vectors. Coordinate transformations of vectors. (Hawking & Ellis)
Topic II: One-forms. Coordinate transformations of 1-forms. N-forms. (Hawking & Ellis)
Topic III: Tensors. Coordinate transformations of tensors. Symmetric and anti-symmetric tensors. (Hawking & Ellis)
Topic IV: Vector basis and dual basis of 1-forms. q-forms. Exterior derivative. Stokes theorem. Correspondence between vectors and 1-forms. (Hawking & Ellis, instructor's notes)
Topic V: Connection. Covariant derivative. Christoffel symbols. (Hawking & Ellis)
Topic VI Metric tensor. Space-time. Christoffel symbols (again). (Instructor's notes, Landau)
Topic VII: Notion of Curvature. Parallel transport. Riemann tensor derivations. (Schutz, Landau)
Topic VIII: Properties of Riemann tensor. Ricci tensor and Ricci scalar. (Hawking & Ellis, Instructor's notes)
Topic IX: Lagrangian in curves space-time. (Landau)
Topic X: Conservation laws in curved space time. (Instructor's notes)
Topic XI: Noether's theorem. Proof. (Bogolubov & Shirkov)
Topic XII: Stress-energy tensor as a consequence of space-time translational invariance. (Bogolubov & Shirkov, Landau)
Topic XIII: Einstein's equation (derivation). (Instructor's notes)
Topic XIV: Newtonian limit. Fixing constants in Einstein's equation (Instructor's notes)
Topic XV: Test of GR. Gravitational redshift. Light bending. Shapiro delay. (Instructor's notes)
Topic XVI: Small perturbations of the metric. Gravitational waves. (Instructor's notes, Landau)
Topic XVII: Emission of gravitational waves. LIGO. (Instructor's notes)
Topic XVIII: Black holes. Schwarzschild black hole (derivation). (Instructor's notes)
Topic XIX: Orbits around Schwarzschild black hole (Instructor's notes)
Topic XX: Falling into Schwarzschild black hole. (Instructor's notes)
Topic XXI: Penrose diagrams (Instructor's notes)

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