Home Page for Physics 171 (General Relativity) for the 2014 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 2014 fall quarter at the University of California, Santa Cruz.


new!!! Final grades for Physics 171 have been assigned. The distribution of all the final course grades is shown below:

course grade distribution

Letter grades are based on the cumulative course average, which is weighted according to: homework (5 problem sets)---40%; midterm exam---25%; and the final exam---35%. This cumulative course average is then converted into a letter grade according to the following approximate numerical ranges: A+ (92.5--100); A (87.5--92.5); A- (82.5--87.5); B+ (77.5--82.5); B (72.5--77.5); B- (67.5--72.5); C+ (62.5--67.5); C(57.5--62.5); D(52.5--57.5); F (0--52.5). Here is the statistical summary of the distribution of the cumulative course averages:

              mean: 74.2               median: 73.2               standard deviation: 9.7               high: 95.3               low : 41.2

Students who did not take the final exam are not included in this statistical summary, but are included in the histogram.

Revised solutions to final exam have been posted to Section IV of this website. Please note that the original solutions omitted some key steps in arriving at the solution to problem 1. This has now been rectified. I also took the opportunity to clean up some notational issues in the solution to problem 2. I also simplified the presentation of the solution to problem 3(b).

Here are the relevant final exam statistics. A histogram of the test scores is shown below:

distribution of final exam scores

Horizontal axis labels correspond to the midpoint value of a bin, which is 10 points wide. Here is the final exam statistical summary:

    exam mean: 60.2           exam median: 64.5           standard deviation: 17.8           highest grade: 86           lowest grade: 25

You can pick up your graded final exams in my office starting on Thursday December 18 after the SCIPP Holiday lunch.

A handout entitled The Cosmological Constant Problem describes the worst prediction in the history of physics. I discussed this briefly in class, and I have now written it up as a little parting gift for the holidays. It has also been posted to Section V of this website.

If you want to learn more about the twin paradox in a Schwarzschild geometry, check out the last entry in Section VIII of this website.

A typographical error that appeared multiple times in the solution to problem 1 of Problem Set 5 has been corrected (replace r/rs with rs/r), and has been re-posted to Section IV of this website.

Table of Contents

[ I. General Information and Syllabus | II. Links to the Web Site for the Textbook | III. Problem Sets and Exams | IV. Solutions to Problem Sets and Exams | V. Other Class Handouts | VI. A Free Book on Tensor Calculus | VII. Free textbooks and lecture notes on general relativity| VIII. 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 Mondays and Thursdays, 2--3 pm
e-mail haber@scipp.ucsc.edu
webpage scipp.ucsc.edu/~haber/

Class Hours

Lectures: Tuesdays and Thursdays, 10--11:45 pm, Nat. Sci. Annex 103

Required Textbook

Relativity, Gravitation and Cosmology, by Robert J.A. Lambourne (Cambridge University Press, 2010).

Course Grading and Requirements

40% regular problem sets
25% Midterm Exam (take-home exam November 13--14, 2014)
35% Final Exam (Monday December 15, 2014, 12--3 pm)

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 Nat. Sci. Annex 103 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

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III. Problem Sets and Exams

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

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IV. Solutions to Problem Sets and Exams

The problem set solutions are available in either PDF or Postscript formats.

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V. Other Class Handouts

By Clifford M. Will (Florida U.). Mar 28, 2014. 113pp.
Published in Living Rev.Rel. 17 (2014) 4
DOI: 10.12942/lrr-2014-4
e-Print: arXiv:1403.7377 [gr-qc] | PDF (arXiv version)| PDF (Journal version)

2. A handout entitled The velocity and momentum four-vectors examines the properties of the velocity and momentum four-vectors of special relativity, and provides a careful derivation of the relativistic law of addition of velocities. In addition, an appendix provides a derivation of the most general Lorentz boost matrix.   [PDF | Postscript].

3. A handout entitled The Cosmological Constant Problem describes the worst prediction in the history of physics. The predicted value of the vacuum energy density (due to quantum fluctuations) is a factor of 10 larger than the observed value. Moreover, if an additional contribution to the vacuum energy exists to cancel off the contribution of quantum fluctuations, the cancellation must be unimaginably precise (accurate to 123 significant figures). This is one of the greatest unsolved problems of fundamental physics.   [PDF | Postscript].


Astrophysical constants and parameters PDF (2 pages)
Experimental tests of gravitational theory PDF (13 pages)
Big Bang cosmology PDF (33 pages)
Cosmological parameters PDF (21 pages)
Dark matter PDF (21 pages)
Dark energy PDF (19 pages)
Cosmic background radiation PDF (24 pages)

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VI. 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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VII. Free textbooks and lecture notes on general relativity

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VIII. Related Web Pages of Interest

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Last Updated: December 18, 2014