Exploring General Relativity: Independent Study Proposal Based on MIT Course

[Reedeegi]

I'm proposing an independent study for my school, and I was wondering if this course seems even possible to do. It follows the MIT 8.962 course, General Relativity, and the Calendar is virtually taken from their syllabus. It goes:

Week 1
Set up computer, familiarize with the text
Week 2
Geometric Viewpoint on Physics in Flat Spacetime: Vectors and Dual Vectors, Tensors;
Special Relativity
Week 3
Geometric Viewpoint on Physics in Flat Spacetime: Energy and Momentum, Conserved Currents, Stress Energy Tensor;
Transformation Law for Tensors
Week 4
Metric in a Curved Space;
Orthonormal and Coordinate Bases; Derivatives; Tensor Densities; Differential Forms and Integration;
Gauge/Coordinate Transformations
Week 5
Metric in a Curved Space (cont.);
Orthonormal and Coordinate Bases; Derivatives; Tensor Densities; Differential Forms and Integration (cont.);
Gauge/Coordinate Transformations (cont.)
Week 6
Connection and Curvature, Geodesics;
Introduction to Curvature
Week 7
Curvature Continued: Geodesic Deviation, Bianchi Identity;
Killing Vectors and Symmetries
Week 8
Einstein's Equation and Gravitation;
Cosmological Constant;
Hilbert Action
Week 9
Weak Field/Linearized General Relativity;
Spacetime of an Isolated Weakly Gravitating Body
Week 10
Gravitational Waves
Week 11
Gravitational Lensing
Week 12
Cosmology;
Distance Measures and Redshift;
Our Universe
Week 13
Schwarzschild Solution;
Birkhoff's Theorem, Metric of a Spherical "Star"
Week 14
Black Holes;
Collapse to Black Hole; Orbits of a Black Hole;
Kerr and Reissner-Nordstrom Solutions
Week 15
Advanced Topics and Current Research in General Relativity
Week 16
Use fragments of thesis and sew them together, choose and plan lecture
Week 17
Deliver lecture; Edit thesis
Week 18
Turn in peer-reviewed thesis

The thesis will be probably 15-25 pages, and the lecture will be approximately 30 minutes long. I plan to meet with an advisor approximately every week, who will assess my knowledge of the topics I learned in the previous week. Does this seem possible? Also, I have DG under my belt, so the only math subject I'd be unfamiliar with would be tensor analysis.

 

[ice109]

I'm proposing an independent study for my school, and I was wondering if this course seems even possible to do. It follows the MIT 8.962 course, General Relativity, and the Calendar is virtually taken from their syllabus. It goes:

Week 1
Set up computer, familiarize with the text
Week 2
Geometric Viewpoint on Physics in Flat Spacetime: Vectors and Dual Vectors, Tensors;
Special Relativity
Week 3
Geometric Viewpoint on Physics in Flat Spacetime: Energy and Momentum, Conserved Currents, Stress Energy Tensor;
Transformation Law for Tensors
Week 4
Metric in a Curved Space;
Orthonormal and Coordinate Bases; Derivatives; Tensor Densities; Differential Forms and Integration;
Gauge/Coordinate Transformations
Week 5
Metric in a Curved Space (cont.);
Orthonormal and Coordinate Bases; Derivatives; Tensor Densities; Differential Forms and Integration (cont.);
Gauge/Coordinate Transformations (cont.)
Week 6
Connection and Curvature, Geodesics;
Introduction to Curvature
Week 7
Curvature Continued: Geodesic Deviation, Bianchi Identity;
Killing Vectors and Symmetries
Week 8
Einstein's Equation and Gravitation;
Cosmological Constant;
Hilbert Action
Week 9
Weak Field/Linearized General Relativity;
Spacetime of an Isolated Weakly Gravitating Body
Week 10
Gravitational Waves
Week 11
Gravitational Lensing
Week 12
Cosmology;
Distance Measures and Redshift;
Our Universe
Week 13
Schwarzschild Solution;
Birkhoff's Theorem, Metric of a Spherical "Star"
Week 14
Black Holes;
Collapse to Black Hole; Orbits of a Black Hole;
Kerr and Reissner-Nordstrom Solutions
Week 15
Advanced Topics and Current Research in General Relativity
Week 16
Use fragments of thesis and sew them together, choose and plan lecture
Week 17
Deliver lecture; Edit thesis
Week 18
Turn in peer-reviewed thesis

The thesis will be probably 15-25 pages, and the lecture will be approximately 30 minutes long. I plan to meet with an advisor approximately every week, who will assess my knowledge of the topics I learned in the previous week. Does this seem possible? Also, I have DG under my belt, so the only math subject I'd be unfamiliar with would be tensor analysis.

how do you know dg but not tensor analysis? they're practically synonymous?

 

[Reedeegi]

how do you know dg but not tensor analysis? they're practically synonymous?

I'm more familiar with vectors and I've done some work in tensors but I feel I need more practice in it.