PHYSICS 3A03

RELATIVITY, GRAVITY AND THE GEOMETRY OF SPACETIME

Undergraduate

Winter 2025 · C01

Topics

Gravity as geometry and the Geometry of Euclidean space: B 1.1 - 1.2; W 1.1-1.4
Special Relativity: physical motivations for the Principle of Relativity B 1.4, 2.1,
Dynamics in special relativity. B 3.2, 3.3
Elementary introduction to Riemannian manifolds W 4.6, 4.7,4.9,
Functions, tangent vectors, one-forms, tensors and tensor fields
The metric tensor; index raising and lowering, computing lengths of curves
Geodesics and the Euler-Lagrange equations
Covariant derivatives B 5.2; W 5.1,5.2, 5.3
Curvature and geodesic deviation B 5.4; W 5.6, 5.7, 5.8
'Physics in curved spacetime B 6.2, 6.3, 6.4
The Einstein field equations, Newtonian limit B 7.1, B 7.2; W 6.2
The Schwarzschild geometry; null and timelike orbits, planetary motion .B 8.1, 8.3, 8.4; W 8.1-8.8
The Schwarzschild black hole solution.. B 8.5; W 9.1-9.4

Introduction to General Relativity
Cosimo Bambi · 2020 · Required
Springer Undergraduate Lecture Notes in Physics · ISBN 978-981-13-1090-4
General Relativity
N.M.J. Woodhouse · 2006 · Required
Springer Undergraduate Mathematics Series · ISBN 1-84628-487-2
Spacetime and Geometry
Sean Carroll · 2019 · any will do · Recommended / optional
Cambridge University Press · ISBN 978-1108488396
Link to textbook ↗
https://textbooks.mcmaster.ca ↗
Free version ↗

Sources