PHYS 428 — Autumn Quarter
Meeting times: Wednesdays and Fridays: 9:00-10.20 am.
Venue: PAB B143
Course Overview: This course introduces the geometric description of gravity encoded by general relativity (GR). We emphasize physical insight, description of curved spacetimes, and calculation of geodesics, the Einstein equations, and their applications to astrophysics and cosmology. Familiarity with multivariable calculus and some introductory special relativity is assumed.
Course Text: James B. Hartle, Gravity: An Introduction to Einstein’s General Relativity.
Learning Goals:
• Develop an understanding of curved spacetime and gravity as geometry.
• Compute and interpret geodesics, curvature, and simple exact solutions.
• Apply GR to black holes, gravitational waves, relativistic stars, and basic cosmology.
Grading & Policies
Homework (weekly): 40%
Midterm (in-class): 30%
Final Paper (topic approved in advance): 30%
Late policy and collaboration guidelines will be discussed in class and posted with the first assignment. You may discuss ideas with peers, but write up solutions independently and cite any resources used.
Planned Topics:
Introduction to gravity and GR
Geometry and physics
Brief review of special relativity
Curved spacetimes and gravity as geometry
Geodesics
Geometry outside spherical stars and black holes
Einstein’s equations
Gravitational waves
Relativistic stars
GR and cosmology
Lecture schedule: (Lecture notes are available on Canvas)
9/24: Introduction to gravity and GR, course roadmap, and motivation. Geometry and physics.
9/26: No class. (added make-up class on 10/6)
10/1: Non-Euclidean geometries and line elements. Minkowski spacetime.
10/3: Introduction to special relativity, inertial frames, and Lorentz transformations.
10/6: Paradoxes and the relativity of simultaneity. Intro to four vectors.
10/8: Four velocity, acceleration, and force. Dynamics in special relativity and the variational principle. Light rays, the Doppler effect, and beaming.
10/10: Curved spacetime and clocks in gravitational fields. Newtonian gravity in spacetime terms.
10/15: Mathematical description of curved spacetime. Four-vectors in curved spacetime and
10/17: Geodesic equation
10/20: Schwarzschild geometry and particle orbits.
10/22: Light rays in curved spacetimes and lensing .
10/24: Gravitational collapse and black holes.
10/31: Event horizon and radial plunge orbits.
11/05: Rotation I
11/07: Rotation II
11/12: Rotating black holes I
11/14: Rotating black holes II and extracting energy from black holes
11/19: Vectors, tensors and the covariant derivative.
11/21: Geodesic deviation and curvature.
11/24: The Einstein equation in vacuum.
11/26: Source of curvature and the Einstein equation with matter.
12/03: Relativisitic stars and emission of gravitational waves.
12/05: Cosmology