Main Textbook: General Relativity (Listed as semi-required)
Good for a one-semester course.
Supplementary readings will be posted here.
Recommended Supplementary Texts:
Bernhard Schutz: A First Course in General Relativity
Edition: Second edition is recommended due to errors in the first.
Contains clever derivations of important geometric objects.
Misner, Thorne, Wheeler (MTW): Gravitation
Used personally by the lecturer but not recommended for beginners.
Good reference but may be dense for new students.
Wald: General Relativity
A mathematically rigorous and self-contained book.
Good for mathematically minded students.
Assessment and Problem Sets
Total Problem Sets: 11
10 worth 9% each, 1 worth 10%
Focus on learning material rather than getting bogged down by grading percentages.
Grading Focus: Entirely based on problem sets, no final exam.
Course Structure
First Half: Mathematical foundations of General Relativity up to Spring Break
Topics will include the derivation of Einstein's field equations.
Aimed at building formalism needed for key applications.
Second Half: Applications of General Relativity
Topics include cosmology, black holes, gravitational waves, and neutron stars.
Introduction to Special Relativity
Goal: Introduce mathematical language with emphasis on the geometric nature of relativity.
First few lectures focus on building a strong formal framework.
Key Concept:
Space-time: A manifold of events endowed with a metric.
Definitions
Manifold: A collection of points with well-understood connectedness properties.
Event: A point in space-time where something happens, defined by coordinates.
Metric: A mathematical object defining distances between events in a manifold.
Inertial Reference Frames
Definition: A lattice of clocks and measuring rods that label events in space-time.
Properties Required:
Moves freely without forces acting on it.
Orthogonal measuring rods with uniform spacing.
Clocks ticking uniformly and synchronized.
Einstein Synchronization Procedure
Method to synchronize clocks based on the constant speed of light.
Any emitted light pulse travels at the same speed (c) in all inertial frames.
Geometric Objects and Vectors
Space-time Vector: Quartet of numbers that transforms between inertial frames.
Defined by how they relate under Lorentz transformations.
Components:
Represented using indices (Greek for space-time, Latin for spatial).
Important Concepts to Remember
Lorentz Transformation: Relationship used to convert between different reference frames.
Dummy Index: An index that is summed over and has no intrinsic meaning.
Free Index: An index that must remain constant on both sides of an equation.
Conclusion
Emphasis on careful definitions and building foundational knowledge in the early weeks will facilitate understanding of more complex concepts later in the course.