General Relativity and Cosmology - Spring 2020

Course
PH471 - General Relativity and Cosmology
Instructor
Ewan Stewart
Email
gr.20s @ profstewart.org
Homepage
http://profstewart.org/gr/
Time
13:00 - 14:30, Tuesdays and Thursdays
Space
Real-time distance classes using Zoom
Teaching assistant
김재권
TA website
http://klms.kaist.ac.kr/course/view.php?id=112826
Questions
Prof: email, Zoom meeting arranged by email
TA: TA website, email, …
Evaluation
class participation, homework submission, presentation, exam

Syllabus and lecture notes

The syllabus and lecture notes will be continually revised. Please make sure you have the latest versions.

  1. Differential geometry
    1. Tensors
      1. Vectors and covectors
      2. Abstract index notation
      3. Metric
    2. Spaces
      1. Tensor fields
      2. Tensor calculus
      3. Bases and coordinates
  2. Relativity
    1. Overview of physics
      1. Map of physics
      2. Newtonian mechanics
    2. Spacetime
      1. Structure of spacetime
      2. Spacetime decomposition
    3. Particles in spacetime
      1. Kinematics
      2. Action
      3. Newtonian decomposition
    4. Dynamics of spacetime
      1. Einstein equation
      2. Matter
    5. De Sitter space
      1. De Sitter metric
      2. Penrose diagrams
    6. Black holes
      1. Schwarzschild metric
      2. Kerr metric
    7. Gravitational waves
      1. Weyl tensor
      2. Plane waves
  3. Cosmology
    1. Expanding universe
    2. Inflation
      1. Motivation
      2. Definition of inflation
      3. Types of inflation
      4. Quantum fields in de Sitter space
      5. Generating perturbations
    3. Origin of matter
      1. Baryogenesis
      2. Dark matter
    4. Accelerating universe

Problems

There will be two submissions for each homework. The teaching assistant will give detailed feedback on each submission.

  1. Newtonian perspective answers
  2. Einstein equation answers
  3. Minkowski space answers
  4. Schwarzschild metric answers
  5. Weyl tensor answers
  6. Expanding universe answers
  7. Inflation answers

Presentation

Prepare a 10 minute presentation on any topic in general relativity or cosmology. LaTeX beamer is recommended.

Deadlines:

Brief review about dark matter and dark energy
조두형
Entropy of black holes
김예찬
Gravitational waves
김태영
Eternal inflation
최현준
Understanding the curvature tensor by using some 2D surfaces in 3D
박주영
Applications of the generalized Gauss-Bonnet-Chern theorem in general relativity
노푸름
Classical tests of general relativity
백종헌
Relativistic stars
조완

Exam

The exam will be open book and will be held via zoom with video at 13:00 to 15:45 on Tuesday 30th June.

Answers

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