Gravitational Physics 2020
The main objective of this course is to discuss some advanced topics in gravitational physics and its applications to high energy physics. Necessary mathematical tools will be introduced on the way.
Course menu & requirements
Study text: First 2 weeks
Study text: first 4 weeks
Study text: all weeks
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
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
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
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
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