Course curriculum

  • 1

    Before we start: course menu & requirements, study text

    • Course menu & requirements

    • Study text: First 2 weeks

    • Study text: first 4 weeks

    • Study text: all weeks
  • 2

    Week 1: Topics in differential geometry

    • Plan for Week 1

    • Lecture 1a: Introduction

    • Lecture 1b: Manifolds and tensors

    • Lecture 1c: Bases and components

    • Lecture 1d: Abstract index notation

    • Lecture 2a: Differential forms

    • Lecture 2b: Levi-Civita n-form

    • Lecture 2c: Application to electromagnetism

    • Lecture 3a: Lie bracket & maps between manifolds

    • Lecture 3b: Lie derivative

    • Lecture 3c: Geometrical meaning of Lie bracket

    • Lecture 3d: Killing vectors

    • Tutorial 1: Differential forms

    • Tutorial 1: upload your notes

    • Tutorial 1: solutions

    • Q&A morning recording: maps between manifolds, inner derivative
  • 3

    Week 2: Cartan's formalism & black holes

    • Plan for Week 2

    • Lecture 4a: Cartan's formalism -- motivating connection, torsion

    • Lecture 4b: Cartan's structure equations

    • Lecture 5a: Applying Cartan - part 1

    • Lecture 5b: Applying Cartan - part 2

    • Lecture 5c: Fixing gauge & Schwarzschild black hole

    • Lecture 5d: Schwarzschild-(A)dS black holes

    • Homework 1: Gravitational waves

    • Lecture 6a: Kerr metric - part 1

    • Lecture 6b: Kerr metric - part 2

    • Tutorial 2: Maxwell and Cartan

    • Tutorial 2: upload your notes

    • Tutorial 2: solutions

    • First 2 weeks survey

    • Q&A Week 2
  • 4

    Week 3: Variational principles & submanifolds

    • Plan for Week 3

    • Lecture 7a: Variational principles -- matter in curved spacetime

    • Lecture 7b: Varying gravitational action

    • Lecture 7c: Brans-Dicke theory

    • Lecture 7d: A few words about dynamical boundary

    • Homework 2: Gauss-Bonnet gravity

    • Lecture 8a: Gauss-Codazzi formalism - part 1

    • Lecture 8b: Gauss-Codazzi -- part 2

    • Lecture 8c: Gibbons-Hawking term

    • Lecture 9a: Introduction to black hole thermodynamics

    • Lecture 9b: Black hole temperature from Euclidean trick

    • Lecture 9c: Black hole entropy from Euclidean action

    • Tutorial 3: Gauss-Codazzi formalism

    • Tutorial 3: Upload your notes

    • Tutorial 3: Solutions
  • 5

    Week 4: Advanced topics 1

    • Plan for Week 4

    • Lecture 10a: Domain wall in flat space

    • Lecture 10b: Self-gravitating domain wall

    • Lecture 10c: Spontaneous compactification of space

    • Lecture 10d: A few words about strings

    • Lecture 11a: Black brane metric ansatz

    • Lecture 11b: Higher-dimensional Schwarzschild solution

    • Lecture 11c: Black string and its potential instability

    • Lecture 12a: Introduction to Kaluza-Klein theory

    • Lecture 12b: U(1) compactification

    • Lecture 12c: KK black holes

    • Lecture 12d: Magnetic black holes & KK monopole

    • Tutorial 4: Kaluza-Klein theory

    • Tutorial 4: Upload your notes

    • Tutorial 4: Solutions

    • Homework 3: Monopoles

    • Q&A morning session
  • 6

    Week 5: Advanced topics 2

    • Plan for Week 5

    • Lecture 13a: Hierarchy problem & large extra dimensions

    • Lecture 13b: Rubakov & Shaposhnikov toy model for fermion confinement

    • Lecture 13c: Israel junction conditions

    • Lecture 13d: Randall-Sundrum brane

    • Lecture 13e: Confinement of gravity

    • Lecture 14a: Gravitational perturbation theory

    • Lecture 14b: Black string instablity

    • Lecture 15a: Quantum mechanical tunnelling

    • Lecture 15b: False vacuum decay in field theory

    • Lecture 15c: Vacuum energy gravitates

    • Tutorial 5: Hawking-Page transition

    • Tutorial 5: Upload your notes

    • Tutorial 5: Solutions