Calendar

WEEK # TOPICS KEY DATES
1

Geometric Viewpoint on Physics in Flat Spacetime: Vectors and Dual Vectors, Tensors

Special Relativity

Problem set 1 out
2

Geometric Viewpoint on Physics in Flat Spacetime: Energy and Momentum, Conserved Currents, Stress Energy Tensor

Transformation Law for Tensors

Problem set 1 due

Problem set 2 out

3

Metric in a Curved Space

Orthonormal and Coordinate Bases; Derivatives; Tensor Densities; Differential Forms and Integration

Gauge/Coordinate Transformations

Problem set 2 due
4

Metric in a Curved Space (cont.)

Orthonormal and Coordinate Bases; Derivatives; Tensor Densities; Differential Forms and Integration (cont.)

Gauge/Coordinate Transformations (cont.)

Problem set 3 out
5

Connection and Curvature, Geodesics

Introduction to Curvature

Problem set 3 due

Problem set 4 out

6

Curvature Continued: Geodesic Deviation, Bianchi Identity

Killing Vectors and Symmetries

Problem set 4 due

Problem set 5 out

7

Einstein's Equation and Gravitation

Cosmological Constant

Hilbert Action

Problem set 5 due

Problem set 6 out

8

Weak Field/Linearized General Relativity

Gauge Invariant Characterization of Gravitational Degrees of Freedom

Spacetime of an Isolated Weakly Gravitating Body

Problem set 6 due

Problem set 7 out

9 Gravitational Waves

Problem set 7 due

Problem set 8 out

10 Gravitational Lensing Problem set 8 due
11

Cosmology

Friedmann-Robertson-Walker Solution; Distance Measures and Redshift

Our Universe

Problem set 9 out
12

Schwarzschild Solution

Birkhoff's Theorem, Metric of a Spherical "Star"

Problem set 9 due

Problem set 10 out

13

Black Holes

Collapse to Black Hole; Orbits of a Black Hole

Kerr and Reissner-Nordstrom Solutions

Problem set 10 due

Problem set 11 out

14 Advanced Topics and Current Research in General Relativity Problem set 11 due