Welcome to the Home Page for Einstein's Relativity

• The first is a listing of some books at a "popular" level, that concern ideas in general relativity.
• The second is a listing of technical books, that are certainly useful, but, as already stated, appeal to various different modes of thinking about the material. All would require some work to use as a text. Some I may occasionally refer to for additional thoughts and insight on a subject.

As already stated, I will be following the text and also the 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.

1. A summary of special relativity, i.e., properties of 4-dimensional spacetime, along with a very useful summary of many conventions about notation that will be used in class, 25 pages.
2. Minkowski diagrams, some help and examples.
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, will be useful and so is given here: Introduction and Conventions on Vectors, Tensors, and Matrices,     23 pages.
6. Introductory comments about tidal gravitational forces, and geometry, 11 pages.
7. 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.
8. Important notes on Covariant Derivatives and Curvature; 73 pages.
   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.
9. Important notes on Structure of the Riemann Curvature Tensor; 14 pages.
   
10. The Lie Derivative on Manifolds, and symmetries of the manifold as generated by Killing Vectors; 16 pages.
11. Various very recent papers concerning the January, 2016 observations by LIGO of gravitational waves emitted as two black holes merged:
    • The original Physical Review Letters paper.
    • Comments from the American Physical Society
    • Comments from the British economics journal, The Economist
    • Comments on the in space telescope, LISA, from The Economist
    • The link posted here is the latest update on the success of the LISA Pathfinder mission to use detectors in orbit to observe gravitational waves.

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

12. 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.
13. A Penrose conformal diagram for the Reissner-Nordström manifold.
14. Discussion of observations made by a uniformly accelerating observer; 15 pages.
15. The Kerr metric, for rotating stellar objects: some rather brief listings of properties and equations; 4 pages.
16. An application for the "Guess" method for calculating affine connections from the orthonormal bases for 1-forms,
    which shows how it does NOT work for the Kerr metric.
    • Penrose conformal diagram for maximal extension of the Kerr manifold
17. 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).
18. A discussion of Lie derivatives and Killing vectors; 15 pages
19. Beginnings of calculations for Weak Gravitational Fields
20. Basic Reviews of Gravitational Waves, by Eanna Flannagan.
21. Notes on Robertson-Walker Spacetimes: 9 pages.
22. Recent Discussions of Current State of Cosmology, by a practicing relativist: George Ellis:
    • Pedagogical discussion of horizons in FRW Cosmologies, written in the American Journal of Physics,, 1993.
    • Excellent review article on the 83 years of General Relativity and Cosmology, 1999: 39 pages.
    • More recent, quite brief summary, 2001---posing questions to be answered
    • A particular explicit model for inflation: the emergent universe, 2003.
    • Brief descriptions of de Sitter and anti-de-Sitter cosmologies, copied from Hawking and Ellis' book on The large scale structure of space-time.
    • References for Work on Cosmologies alternative to the FLRW (isotropic and homogeneous) model.

Exams and Homework Assignments: There will be two examinations,
In addition, there will be (more or less) weekly homework assignments, with solutions posted after they have been turned in.
The grader is Jaksa Osinski, who can be emailed by clicking on his name. He will be at our weekly problem sessions, for help, and will have an office hour once per week, on Mondays, from 11-12 AM, in the department lobby.

• The Albert Einstein Institute, at the Max-Planck Institut in Potsdam, Germany.
• the most important journal in the field is Classical and Quantum Gravity, published by the Institute of Physics in Great Britain.
• Astrophysical Gravitational Wave Sources: NASA Data Archive, and information about LISA, the projected, orbiting gravitational wave telescope.
• Historical Exhibit on Albert Einstein, from the American Institute of Physics.
• Very interesting discussion and movies of both orbiting around and falling into a black hole can be found on the website, maintained by Andrew Hamilton (Univ. Colo.). It also has many other interesting links about special and general relativity.
• Some interesting movies showing the fact that when one uses light rays to view very-fast-moving, 3-dimensional objects they appear to rotate, were made by Leo Brewin at Monash University in Australia. I have copied two of the movies that I liked the best, which may be found here:
  • for a fast-moving Rubik's Cube moving toward you, and
  • for a fast-moving steam locomotive moving past you.
  They move fast; therefore, it is most interesting if you actually slowly "drag" the play button along while watching.
• An interesting history of the ideas in general relativity, beginning with Aristotle and Copernicus, along with many further links to biographical information on the researchers involved, can be found at this link, created by people at St. Andrews University in Scotland.
• Finley's page of Other Interesting Links for Relativity
• From time to time, a student asks a question which is too complicated to fully discuss in class.
  If possible I will then create a webpage with a listing of articles appropriate to answering that question.
  At the beginning of the semester there were two such listings here.
  • Questions about "warp drives";
  • Questions concerning Reality and Stability of Black-Hole Interiors
  • Freely Falling, or Supported Charges Do Not Radiate in a Gravitational Field: this does not violate the Equivalence Principle.
    This paper seems to provide a correct answer to an old and somewhat controversial question.
    Some earlier responses to this question are in this paper.
  • Questions somewhat related to the radiation of charges are those concerning the backreaction of particles in a gravitational field. They are discussed very carefully and rigorously in this paper of Eric Poisson.
  • Is the concept of a graviton---as a spin 2, massless object "something like" a photon" really an idea consistent with full, nonlinear general relativity?
    This paper says no, although this is still a very controversial issue.
  • deSitter and anti-deSitter spacetimes are described in these 11 pages from Hawking and Ellis' book.
    This put here since there were quite a few questions about it at the last class, and there wasn't really time to discuss it more.
    However, the new book by Griffiths and Podolsky, listed in my online list of other books, is much more complete on this question.
  • Very interesting history of Gravity Probe B, As well, there is. a review article from IOP Science

• Astronomy Picture of the day
  • Index to the complete list of their pictures.
• COBE satellite data on cosmic microwave background
• Very interesting background primer on Cosmology and the astronomical measurements that allow us to make inferences about it.
• The official webpage for the LIGO observatory for gravitational waves, otherwise known as the Laser Interferometer Gravitational Wave Observatory, built at Livingston, LA, and Hanford, WA.

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