|
ASTRON 445-1,2 General Relativity and Applications
Open to all advanced undergraduates and graduate students in Physics and Astronomy, Math, and related fields.
Instructor: Prof. Frederic Rasio (Dearborn Rm 22; Office hour: Wednesdays 2-3 PM)
Grader: Vivien Raymond (Dearborn Rm 5; Office hour: Mondays 3-4 PM)
Textbook: "Gravity" by James B. Hartle (Addison-Wesley)
Einstein's relativistic theory of gravity is
almost a century old. At its core is one of the most beautiful and revolutionary
concepts of modern science -- the idea that gravity is the geometry
of our four-dimensional spacetime.
This introduction to General Relativity will be taught using
an innovative approach, pioneered by Hartle, where the simplest
and most important solutions of the Einstein equation are
introduced first, without derivation, bringing the students to the
interesting physical phenomena as quickly as possible. The Einstein field equation and many of the mathematical details are introduced
later, and solutions are then derived to show how these geometries originate.
With this approach, advanced undergraduate students with a
solid background in classical physics should be able to take at
least the first (self-contained) quarter of the course, and all students
will find the material much more enjoyable than in the more
traditional "math first" approach.
Syllabus:
First Quarter
- Review of Special Relativity and Newtonian Gravity
- Gravity as Geometry of Curved Spacetime
- Geodesics and Conservation Laws
- Schwarzschild Geometry
- Tests of GR and the PPN Formalism
- Gravitational Collapse and Black Holes
- Rotating Black Holes and the Kerr Geometry
- Black Hole Interiors, Penrose Diagrams
Second Quarter
- Differential Geometry, Tensors, Covariant Derivatives
- Riemann Curvature and the Field Equation in Vacuum
- Energy-Momentum Tensor, The Einstein Equation
- Perturbation Theory, Gauge Transformations
- Emission of Gravitational Radiation
- More advanced applications, as time permits, such as: Relativistic Stars, TOV equation and the Chandrasekhar Limit; Relativistic Hydrodynamics; ADM Formalism and Numerical Relativity; Quantum Mechanics in Curved Spacetime; Inflationary Cosmology.
|
