## Course curriculum

• 1

### Before we start: course plan, requirements, study text

• Welcome: Course plan and requirements

• Course Menu & Requirements

• PSI study text

• 2

### Week 1: First look at GR

• 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

• 3

### Week 2: Differential geometry

• 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

• Tutorial 2: Upload your notes

• 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

• Tutorial 3: Upload your notes

• 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

• 4

### Week 3: General relativity

• 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

• Tutorial 4: Upload your notes

• 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

• Tutorial 5: Upload your notes

• 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

• 5

### Week 4: Applications

• 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

• Tutorial 6: Upload your notes

• 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

• Tutorial 7: Upload your notes

• 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

• 6

### Week 5: Advanced topics

• 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

• Tutorial 8: Upload your notes

• 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

• 7

### Interviews

• List of questions

• Interview Schedule