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Welcome: Course plan and requirements

Course Menu & Requirements

PSI study text

Plan for Week 1

Lecture 1a: Conceptual path to the theory

Lecture 1b: Principle of equivalence: Einstein's elevator

Lecture 1c: Gravitational redshift & Light bending

Lecture 1d: Brief summary

Lecture 1e: Local inertial (freely falling) frame

Lecture 1f: Geodesic equation

Lecture 1g: Curved metric and Christoffel symbols

Lecture 2a: Newtonian limit

Lecture 2b: Gravitational redshift again

Lecture 2c: Brief summary

Lecture 2d: Fake gravity: first look at Rindler

Tutorial 1: Doppler and gravitational redshifts

Tutorial 1: Upload your notes

Tutorial 1: Solutions

Homework 1: Equivalence principle at work - charge in a lab

3a: True vs. fake gravity

3b: Field theory for gravity

Lecture 3c: Introduction to differential geometry: manifolds

Lecture 3d: Maps, curves, and surfaces

Plan for Week 2

Lecture 4a: Brief summary

Lecture 4b: Tensors - part 1

Lecture 4c: Tensors- part 2

Lecture 4d: Connection

Tutorial 2: Some differential geometry

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Tutorial 2: Solutions

Lecture 5a: Metric

Lecture 5b: Brief summary

Lecture 5c: Invariant volume element

Lecture 5d: Parallel transport & Killing vectors

Tutorial 3: The connection

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Tutorial 3: Solutions

Lecture 6a: Motivating the metricity condition and curvature

Lecture 6b: Riemann tensor

Lecture 6c: Brief summary

Lecture 6d: Rabbits and relations

Lecture 6e: First look at cosmological constant

Lecture 6f: General relativity: particle in curved space

Plan for Week 3

Lecture 7a: Geodesic deviation equation

Lecture 7b: Fields in curved space

Lecture 7c: Rosenfeld's energy momentum tensor

Lecture 7d: Example 1 -- scalar field

Lecture 7e: Example 2 -- electromagnetism in curved space

Lecture 7f: Example 3 -- perfect fluid

Tutorial 4: Tensorial beasts of GR

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Tutorial 4: Solutions

Lecture 8a: Einstein-Hilbert action

Lecture 8b: Palatini formalism & other remarks on Einstein-Hilbert action

Lecture 8c: Einstein equations with matter

Lecture 8d: Bianchi identities

Lecture 8e: Bianchi identities in action -- how many evolution equations?

Lecture 8f: Conservation laws

Tutorial 5: Killing vectors and Maxwell in curved space

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Tutorial 5: Solutions

Lecture 9a: A few remarks on energy conditions

Lecture 9b: Linearized gravity -- brief comments on your homework

Lecture 9c: Gravitational waves - gauge fixing

Lecture 9d: Gravitational waves - 2 polarizations

Homework 2: Linearized gravity

Plan for Week 4

Lecture 10a: Radiative fields from an isolated system

Lecture 10b: Remarks on spin and radiation

Lecture 10c: Energy of gravitational field -- Landau & Lifshitz prescription

Lecture 10d: Perturbative construction of gravitational energy momentum tensor

Lecture 10e: Quadrupole radiation formula

Tutorial 6: Gauge fixing

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Tutorial 6: Solutions

Lecture 11a: Schwarzschild solution & Birkhof's theorem

Lecture 11b: Singularities of Schwarzschild solution

Lecture 11c: Schwarzschild solution at work -- first verifications of GR

Lecture 11d: Geodesics in Schwarzschild

Lecture 11e: Perihelion shift of Mercury

Tutorial 7: Linearized gravity

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Tutorial 7: Solutions

Lecture 12a: Black holes -- introductory remarks

Lecture 12b: Rindler horizon as a surface of infinite redshift

Lecture 12c: Maximal extension of Rindler space

Lecture 12d: Basic features of Schwarzschild black hole

Lecture 12e: Einstein-Rosen bridge

Lecture 12f: A few remarks on astrophysical black holes

Homework 3: Light bending in Newton's and Einstein's gravity

Plan for Week 5

Lecture 13a: Schwarzschild black hole -- 1st law of black hole mechanics

Lecture 13b: Four laws of black hole mechanics

Lecture 13c: Bekenstein's entropy and Hawking's discovery

Lecture 13d: Unruh temperature via Euclidean trick

Lecture 13e: Euclidean derivation of the area law

Tutorial 8: Black holes

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Tutorial 8: Solutions

Lecture 14a: Remarks on Hawking radiation

Lecture 14b: Black hole information paradox Part I - Hawking vs. Page curve

Lecture 14c: Black hole information paradox Part II - information recovery

Lecture 14d: Brief summary of the course

List of questions

Interview Schedule