Welcome To Our Course!
PHYS 225B: General Relativity
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About this course

Practical Information

Time and Place

Mayer Hall 5301
Monday and Wednesday, 12:30- 1:50


There will be a homework assigned every 2-3 weeks (approximately)
There will be a final project or take home exam
Grade will be a combination of 60% homework, 30% final project/exam, 10% participation

Office Hours

Monday & Wednesday: 4pm
With: Prof. Grinstein
Mayer Hall 5230
Office hours will continue until the earlier of 4pm or all students leaving
Additional office hours will be arranged upon request

Course Description

From the UCSD course catalogue: This is a two-quarter course on gravitation and the general theory of relativity. The first quarter is intended to be offered every year and may be taken independently of the second quarter. The second quarter will be offered in alternate years. Topics covered in the first quarter include special relativity, differential geometry, the equivalence principle, the Einstein field equations, and experimental and observational tests of gravitation theories. The second quarter will focus on more advanced topics, including gravitational collapse, Schwarzschild and Kerr geometries, black holes, gravitational radiation, cosmology, and quantum gravitation.

Homework and Exams

And Solutions


  1. Due January 21 (Solutions)
  2. Due February 9 (Solutions)
  3. Due February 23 (Solutions)
  4. Due March 9 (Solutions)



Course notes prepared by the instructor. At students' request I have scanned my lecture notes. Be advised that they are written for my own use, so they tend to have scratches and corrections and marginal notes that may be irrelevant! If anyone wants to transfer them to LaTeX please get in touch with the instructor.

You may also want to use your favorite search engine to look for General Relativity Lecture Notes.
For example, you can find there Notes by Sean Carroll and by Sergei Winitzki.

Chapter 1: Mathematical review


Review of elements of differential geometry. Maps between manifolds, pull-back, push forward. Diffeomorphisms. Derivatives without connection: exterior and Lie. Isometries, Killing Vectors.

Chapter 2: Maximally symmetric spaces


Generalities. Minkowski space as an excuse to learn about causal structure and Penrose diagrams. de Sitter space. Causality (out of order). Horizons. Anti de Sitter space.

Chapter 3: Elements of Cosmology


Homogeneous and Isotropic Spaces. FRW metric. Friedmann Equations. Distance measurements; Age of Universe.

Chapter 4: Black Holes I


Schwarzschild Metric. Birkhoff's Theorem. Singularities. Geodesics. Red Shift. Kruskal coordinates and extension. Penrose Diagrams.

Chapter 5: Black Holes II


More General Black Holes. Charged Holes. Spinning Holes. Penrose Process, Hawking Temperature.

Chapter 6: Other topics??


Tetrads, spinors, etc. Singularity theorems. Hawking radiation.

Textbooks on Reserve

There are many texts on General Relativity. You can read for free some that can be viewed on-line: go to the Roger on the UCSD library web page, and search for "General Relativity" or the like and select "Electronic materials." You must be on the UCSD network to access these materials.
Here are some hardcopy texts that I have placed on Reserve at Geisel Library.

Robert M. Wald

General Relativity

Steven Weinberg

Gravitation And Cosmology: Principles And Applications Of The General Theory Of Relativity

Anthony Zee

Einstein gravity in a nutshell

Sean Carroll

Spacetime and geometry: an introduction to general relativity

S. W. Hawking & G. F. R. Ellis

The Large Scale Structure Of Space-Time

Charles W. Misner, Kip S. Thorne, John Archibald Wheeler


Bernard F. Schutz

A First Course In General Relativity

Our Amazing Team

The Instructor, Teaching Assistants, Administrative Support: all rolled into one!

Benjamin Grinstein

Distinguished Professor of Physics

Prof . Grinstein is a Theoretical Physicist. His main research interests are in the areas of particle physics and cosmology. Learn more about his recent work on his website.

Contact The Team

Of course, students know how to contact "the team" anyway.