Welcome to the Home Page for Physics 570

Spring, 2016
Monday, 2:00 PM - 3:30 PM, and Wednesday, 2:00 PM - 2:55 PM, in Room 184;
Office Hours: Mon. & Tues.: 3:30-4:30 PM; Wedn. 1 - 1:50 PM.

Albert Einstein (1879 - 1955)

spacetime diagram
for two black holes
colliding to become one

Einstein with Tagore

General Introduction

The purpose of this class:
This class will provide an overview of the theory of general relativity, Einstein's theory of relativistic gravity, as well as some basic applications, including at least the solar-system tests of gravitational theories,some of the more interesting properties of black holes and gravitational waves, along with some surveys of cosmology.

This class will not completely prepare you for research in this area: it will be an overview with insufficient depth for that purpose.
     However, that is more likely than not exactly what you wanted anyway.

  The first third to half of the course will focus primarily on the basic structure of the theory, with relevant physical motivation and insight thrown in along the way, and also provide a reasonable introduction to the needed mathematics. You do NOT need to already know more physics and mathematics than is described in the Prerequisite section just below. The major applications will come after that, although perhaps some discussion of motions around spherical stars, and weak gravitational waves will come in the earlier sections.
I assume you have a good foundation in standard undergraduate physics: classical mechanics, electromagnetism, and the usual junior-level special relativity. Also you should have a mathematics background in calculus, differential equations, and linear algebra. The mathematics of general relativity is differential geometry, but I am not assuming you have had any studies on that before: we will spend a good fraction of the first portion of the course learning the relevant differential geometry.
An extended/advanced course in special relativity is NOT necessary. Only the basic ideas of spacetime, 4-vectors, Minkowski diagrams, etc. are needed from special relativity; our time will mostly be concerned with questions involving gravitational fields in 4-dimensional spacetime.

Textbooks and Syllabus:

  • As already stated, I will actually be following handouts of my own creation, presented as pdf-files on this website, which should be read, at least more or less, in the order listed below.
  • Handouts to supplement the texts: parts of the course will follow these closely.
    They are Acrobat-readable (*.pdf) files that you should print out, at appropriate times during the course of the class.
    1. Introductory comments about tidal gravitational forces, and geometry, 11 pages.
    2. A brief review of special relativity, along with some notational conventions, 25 pages, somewhat revised.
    3. Some notes on the Lorentz group and its subgroup, rotations in 3-space   28 pages.
    4. A useful summary of the Lorentz transformations of several useful physical quantities, 6 pages.
    5. While I have discussed some notations for vector spaces and matrices in the review of special relativity, it is hoped that a complete summary of such things, including comments about the Levi-Civita symbol and determinants of matrices is given here: Introduction and Conventions on Vectors, Tensors, and Matrices,     23 pages, revised 3 Febr., 2016.
    6. In some sense all of the above handouts have dealt with review, or physical motivation. At this point we begin considering the mathematical needs for general relativity! Tangent Vectors and Differential Forms over Manifolds     33 pages.
    7. Important notes on Covariant Derivatives and Curvature; 73 pages. revised only slightly, 23 Febr., 2016.
      This contains the physical interpretations for the ideas named in the title, and is extremely important.
      It also has the clearest discussion of (non-holonomic) tetrad basis sets, best for physical interpretations of components of vectors.
    8. Some useful notes on ways to view the curvature tensor, and its parts.
    9. Various very recent papers concerning the January, 2016 observations by LIGO of gravitational waves emitted as two black holes merged:

      From here on, the handouts consider various specific applications to physical systems.

    10. A summary of local properties of spherically symmetric, static spacetimes; 9 pages;
      and also some notes on the Kruskal extensions.
      and some figures showing light cones along radial, inward trajectories in both Schwarzschild and Kruskal coordinates,
      as well as a Maple file that can be downloaded and run, showing radial, inward timelike trajectories in considerable detail.
    11. A Penrose conformal diagram for the Reissner-Nordström manifold.
    12. Discussion of observations made by a uniformly accelerating observer; 15 pages.
    13. The Kerr metric, for rotating stellar objects: some rather brief listings of properties and equations; 4 pages.
    14. the important, original paper on rotating black holes:
      Rotating Black Holes: Locally Nonrotating frames, energy extraction, and scalar synchrotron radiation
      by James M. Bardeen, William H. Press, and Saul A. Teukolsky, The Astrophysical Journal, 178, 347-369 (1972).
    15. An invited paper on colliding(plane) gravitational waves by Valería Ferrari, presented at the 1989 conference of the Society for General Relativity and Gravitation (GRG), in Boulder, Colorado.
    16. A discussion of Lie derivatives and Killing vectors; 15 pages
    17. All the notes below here concern many different opinions on the very intriguing subject of Cosmology:

    Exams and Homework Assignments: There will be two examinations, currently scheduled for 21 March and 27 April, but no final examination.
    In addition, there will be (more or less) weekly homework assignments, with solutions posted after they have been turned in.
    The grader for the course is (Stephen) Keith Sanders. If you wanted to speak with him, note that he usually attends class, but you could also email him for a meeting time and place.

    Homework Assignments Due Date Homework Solutions
    HW #1, due 27 Jan. Solutions for HW #1
    HW #2, extended due 3 Febr. Solutions for HW #2
    HW #3, due (Monday) 15 February. Solutions for HW #3
    HW #4, due (Monday) 22 February. Solutions for HW #4
    HW #5, due (Wednesday) 2 March. Solutions for HW #5
    HW #6, due (Wednesday) 9 March. Solutions for HW #6
    An Exam on Monday, 21 March, 2016
    You may bring any personally-written material with you, or my handouts for this class.
    Solutions are available here.
    HW #7, due (Monday) 28 March. Solutions for HW #7
    HW #8, due (Monday) 11 April. Solutions for HW #8
    HW #9, due (Wednesday) 20 April. Solutions for HW #9
    Exam 2 (Take Home) is due on Wednesday, 4 May, 2016
    It is due at the beginning of class that day.
    You may NOT consult with any humans other than myself;
    Solutions are here
    Usable Maple files are downloadable; they require a right-click on the link, and then choosing "Save link as ...".

    Homework assignments and Solutions are pdf-files, except when occasionally there will be an html-file for a portion of the solutions.
    Solutions will be made available once the assignments have been turned in.
    Homework is DUE at the beginning of the class period on the due date!

    There are many modern software packages to perform tensor calculations.
    I prefer the program grtensor, which is described in more detail in this linked webpage.
    After you have a reasonably-good understanding of how the process works, I see no reason why you shouldn't have an algebraic computing system do the work for you.

    Links to Worldwide Relativity Information Sites

    Links to Exciting Astronomy News

    Click here to mail your comments and suggestions concerning the Homepage Click here to go to Finley's own Home Page Click here to go to the Physics and Astronomy Department Home Page.

    Last updated/modified: 19 January, 2016