Home Page for Physics 171 (General Relativity) for the 2003 Fall Quarter

This page contains copies of the class handouts, and other items of interest to the Physics 171 class. This course is being offered during the 2003 fall quarter at the University of California, Santa Cruz.

All the material on this web site is available either as a postscript or as a PDF file. Instructions for viewing and printing such files are provided below.


The final exam solutions are now available. Enjoy your holiday break! You earned it!!

Table of Contents

[ I. General Information and Syllabus | II. Links to the Web Site for the Textbook | III. Instructions for Viewing and Printing Files | IV. Problem Sets and Exams | V. Solutions to Problem Sets and Exams | VI. Other Class Handouts | VII. A Free Book on Tensor Calculus | VIII. Interesting Figures | IX. Related Web Pages of Interest]

I. General Information and Syllabus

The General Information and Syllabus handout is available in either PDF or Postscript format     [PDF | Postscript]
Some of the information in this handout is reproduced here.

General Information

Instructor Howard Haber
Office ISB 326
Phone 459-4228
Office Hours Monday 3--4 pm and Tuesday, 11 am--12 noon
e-mail haber@scipp.ucsc.edu

Class Hours

Lectures: Tuesdays and Thursdays, 2--3:45 pm, ISB 231

Required Textbook

Gravity: An Introduction to Einstein's General Relativity, by James B. Hartle (Addison Wesley, 2003)

Course Grading and Requirements

40% regular problem sets
25% Midterm Exam (take-home exam November 4--6, 2003)
35% Final Exam (Tuesday December 9, 2003, 8--11 am)

Problem sets will be handed out on a regular basis. The homework problem sets are not optional. You are encouraged to discuss the class material and homework problems with your classmates and to work in groups, but all submitted problems should represent your own work and understanding.

The final exam will be held in ISB 231 and will cover the complete course material. You must take the final exam to pass the course.

Course Syllabus

The course outline is available in either PDF or Postscript format     [PDF | Postscript]

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II. Links to the Website of the Textbook

Home Page of Hartle's textbook

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III. Instructions for Viewing and Printing Files

To view and print postscript files, you will need to obtain the program ghostscript and a viewer appropriate for your machine ( e.g., ghostview or gv for unix and linux, GSview for Windows, or MacGSView for Macintosh operating systems). If you are running a unix or linux operating system, then ghostview or gv should already exist on your computer (a version of GSview is also available for linux). If you do not have the required programs, go to http://www.cs.wisc.edu/~ghost/ and download the programs appropriate for your computer. Note that GSview and MacGSView also allow you to print postscript files on almost printer (including non-postscript printers).

To view and print PDF files, you need to use Adobe Acrobat Reader, a free program that can be obtained from Adobe Systems Incorporated at http://www.adobe.com/products/acrobat/readstep.html. On a unix or linux machine, the Adobe Acrobat Reader program (called acroread) may already be installed on your system. It should be noted that the postscript viewing programs gv, GSview and MacGSView (see above) can also view and print PDF files.

Finally, you may wish to set up your web browser so it can automatically view postscript and PDF files. When Adobe Acrobat Reader is installed on your system, it should install a plugin that allows you to view pdf files inside your web browser automatically. To view postscript files, you can either save the files and then view them, or instruct your browser the first time it encounters a postscript file by selecting "open" and then specify the location of the postscript viewer program. In Netscape, you can set this up manually by selecting Edit/Preferences/Navigator/(Helper) Applications from the menu and edit the application/postscript entry to indicate the location of the postscript viewer program. Type in the name of the executable followed by a space and then %s and then press OK.

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IV. Problem Sets and Exams

Problem sets and exams are available in either PDF or Postscript formats

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V. Solutions to Problem Sets and Exams

The scanned versions of handwritten problem set and exam solutions are available in PDF format:

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VI. Other Class Handouts

By Clifford M. Will (Washington U., St. Louis). Mar 2001. 103pp.
Published in Living Rev.Rel.4:4,2001
e-Print Archive: gr-qc/0103036

References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Citation Search
Abstract and Postscript from Los Alamos (mirrors: au br cn de es fr il in it jp kr ru tw uk aps )
CERN Library Record

By Naresh Dadhich (Ganeshkhind, IUCAA). IUCAA-10-2001, Jan 2001. 26pp.
Seventh Vaidya-Raychaudhari Endowment Award Lecture.
Lectures given at 21st Meeting of the Indian Association for General Relativity and Gravitation (IAGRG 2001), Nagpur, India, 30 Jan - 1 Feb 2001.
e-Print Archive: gr-qc/0102009

References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX
Abstract and Postscript from arXiv.org (mirrors: au br cn de es fr il in it jp kr ru tw uk aps )
CERN Library Record
Conference Info

By Joan Sola (Barcelona Autonoma U., IFAE). UAB-FT-499, Jan 2001. 16pp.
Invited talk given at EURESCO Conference on Frontiers in Particle Astrophysics and Cosmology, San Feliu de Guixols, Spain, 30 Sep - 5 Oct 2000.
Published in Nucl.Phys.Proc.Suppl.95:29-37,2001 Also in *San Feliu de Guixols 2000, Frontiers in particle astrophysics and cosmology* 29-37
e-Print Archive: hep-ph/0101134

References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Citation Search
Abstract and Postscript from arXiv.org (mirrors: au br cn de es fr il in it jp kr ru tw uk aps )
CERN Library Record
Nuclear Physics Electronic
Conference Info

By Palash B. Pal (Saha Inst.). SINP-TNP-99-22, May 1999. 12pp.
Invited talk at Meeting on Recent Developments in Neutrino Physics, Ahmedabad, India, 2-4 Feb 1999.
Published in Pramana 54:79-91,2000
e-Print Archive: hep-ph/9906447

References | LaTeX(US) | LaTeX(EU) | Harvmac | BibTeX | Keywords | Citation Search
Abstract and Postscript from arXiv.org (mirrors: au br cn de es fr il in it jp kr ru tw uk aps )
CERN Library Record
Conference Info


Astrophysical constants Postscript PDF (7 pages)
Experimental tests of gravitational theory Postscript PDF (11 pages)
Big Bang cosmology Postscript PDF (28 pages)
Big-bang nucleosynthesis Postscript PDF (11 pages)
Global cosmological parameters: H0, Omega, and Lambda Postscript PDF (17 pages)
Dark matter Postscript PDF (11 pages)
Cosmic background radiation Postscript PDF (13 pages)

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VII. A Free Book on Tensor Calculus

A free textbook entitled Introduction to Tensor Calculus and Continuum Mechanics by John H. Heinbockel is available via the links below. Check it out if you would like more practice in using tensors and manipulating indices.

The above files are zip files that should be unzipped on a Windows based PC. You should be warned that I have not succeeded in printing out any of the above files obtained after unzipping (although they can be viewed successfully with acrobat reader or ghostview). For your convenience, each chapter of the book appears separately as a pdf and a postscript file below. I made the pdf files from the postscript (rather than use bookpdf.zip) and I was able to print out the resulting pdf files.

Part 1 contains the book cover, preface and a table of contents. Parts 2--5 cover topics of tensor algebra and calculus and Part 6 introduces some differential geometry and applies it to general relativity. Parts 7--12 cover topics of continuum mechanics. Part 13 is the bibliography and three appendices and Part 14 is the index.

Title, preface and table of contents
Index Notation
Tensor Concepts and Transformations
Special Tensors
Derivative of a Tensor
Differential Geometry and Relativity
Tensor Notation for Vector Quantities
Basic Equations of Contiuum Mechanics
Contiuum Mechanics (Solids)
Contiuum Mechanics (Fluids)
Electric and Magnetic Fields
Bibliography and Three Appendices

WARNING! You may receive a printer error if you try to print the postscript files above. To obtain a hard copy of these chapters, I recommend printing the pdf files.

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VIII. Interesting Figures

1. Constraints on the cosmological parameters: a summary figure--version 1 (postscript version)

cosmological parameters
The average density of matter (horizontal axis) versus the energy density in the cosmological constant (vertical axis). Their sum gives the total cosmic energy content and determines the geometry of spacetime (blue line). Their difference characterizes the relative strength of expansion and gravity, and determines how the expansion rate evolves with time (teal line). Recent observations (the green, yellow and purple regions) constrain the cosmological parameters. A balance between the two densities determines the fate of the universe (red line). All observations seem to favor a narrow region of parameter space close to the point marked "new preferred model". The old standard model of a flat universe with zero cosmological constant appears to be ruled out. Taken from J. Garcia-Bellido, astro-ph/9906497.

2. Constraints on the cosmological parameters: summary figures--version 2 (postscript version)

combined data     age of universe
(a) Combined data from Type Ia supernovae, CMBR and clustered matter observations. It is seen that the FRW cosmological models with positive cosmological constant and forever expanding are favored; (b) Type Ia supernovae data as in (a) showing that the preferred model is an accelerating universe about 14 Gyr old. Both figures were given in a review article by J. Sola hep-ph/0101134. I have updated figure (a) to one that includes the most recent data.

3. The Horizon Problem of Standard Big-Bang Cosmology Illustrated (postscript version)

horizon problem
Perhaps the most acute problem of the big bang is explaining the extraordinary homogeneity and isotropy of the cosmic microwave background radiation (CMBR). Information cannot travel faster than the speed of light, so the causal region (so-called horizon or Hubble radius) at the time of photon decoupling could not be larger than about 300,000 light-years across, or about one degree projected on the sky today. So why do regions that are separated by more than one degree in the sky have the same temperature, when the photons that come from those two distant regions could not have been in causal contact when they were emitted? This constitutes the so-called horizon problem, which is spectacularly solved by inflation. Taken from a review article by Juan Garcia-Bellido astro-ph/9906497.

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IX. Related Web Pages of Interest

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Last Updated: December 9, 2003