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 2015 fall quarter at the University of California, Santa Cruz.
I have added some clarifications to the solutions of problems 3(c) and 5 of Problem set 4 (along with some interesting references to the literature). The solutions to Problem set 4 have been reposted to Section IV of this website.
Problem set 5 has been posted to Section III of this website.
A typographical error in the solutions to Problem set 3 has been corrected. The revised solution set has been reposted to Section IV of this website.
A first draft of a new handout entitled Parallel Transport and Curvature has been posted to Section V of this website. I provide this handout in order to provide more details on the connection (no pun intended) between parallel transport of a vector along a closed loop and the curvature tensor.
Solutions to midterm exam have been posted to Section IV of this website.
A handout entitled The Cosmological Constant Problem discusses some of the implications of adding a cosmological constant to Einstein's field equations of general relativitiy. In particular, the handout discusses why the cosmological constant is so problematical for fundamental physics. This handout has also been posted to Section V of this website.
Is energy conserved in general relativity? The answer to this question is not straightforward. Check out some relevant links that have been added to Section VIII of this website.
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  4594228  
Office Hours  Mondays and Tuesdays, 23 pm  
haber@scipp.ucsc.edu  
webpage  scipp.ucsc.edu/~haber/  
TA  Adam Coogan  
Office  ISB 320  
Phone  4594762  
acoogan@ucsc.edu  
Lectures: Tuesdays and Thursdays, 121:45 pm, Nat. Sci. Annex 102
Discussion Section: Wednesdays, 56:10 pm, Thimann 101
Relativity, Gravitation and Cosmology: A Basic Introduction, second edition, by TaPei Cheng (Oxford University Press, 2010).
The most recent compilation of the errata to the 2014 reprinting of the second edition of the textbook can be found here: [PDF]
If you have the first printing of the second edition, please consult the webpage of Cheng's textbook for the relevant errata.
40% regular problem sets
25% Midterm Exam (takehome exam: pick up evening of November 6, 2015;
return morning of November 9, 2015)
35% Final Exam (Tuesday December 8, 2015, 811 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 Nat. Sci. Annex 102 and will cover the complete course material. You must take the final exam to pass the course.
The course outline is available in either PDF or Postscript format
[PDF
 Postscript]
Problem sets and exams are available in either PDF or Postscript formats
The problem set solutions are available in either PDF or Postscript formats.
1. THE CONFRONTATION BETWEEN GENERAL RELATIVITY AND EXPERIMENT.
By Clifford M. Will (Florida U.). Mar 28, 2014. 113pp.
Published in Living Rev.Rel. 17 (2014) 4
DOI: 10.12942/lrr20144
ePrint: arXiv:1403.7377
[grqc]  PDF (arXiv
version) PDF
(Journal version)
2. A handout entitled The velocity and momentum fourvectors examines the properties of the velocity and momentum fourvectors 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, How do the connection coefficients transform under a general coordinate transformation?, derives the transformation law for the connection coefficients with respect to general coordinate transformations. The transformation law contains an inhomogeneous piece, which implies that the connection coefficients are not the components of a tensor. Nevertheless, this inhomogeneous piece is critical in establishing two results. First, the connection coefficients vanish in the local inertial frame. Second, presence of the connection in the definition of the covariant derivative is precisely what is needed so that the covariant derivative of a tensor is also a tensor. [PDF  Postscript].
4. A handout entitled Parallel Transport and Curvature presents the details of the calculation that demonstrates the connection (no pun intended!) between the change in a vector parallel transported around an infinitesimal closed loop and the Riemann curvature tensor. The derivation presented is slightly more general than the one given in Box 13.2 on pp. 311312 of our textbook. [PDF  Postscript].
5. A handout entitled The
Cosmological Constant Problem discusses some of the
implications of adding a cosmological constant to Einstein's field
equations of general relativitiy. In particular, the handout
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
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 25 cover topics of tensor algebra and calculus and Part 6 introduces some differential geometry and applies it to general relativity. Parts 712 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  

Dynamics  

Basic Equations of Contiuum Mechanics  

Contiuum Mechanics (Solids)  

Contiuum Mechanics (Fluids)  

Electric and Magnetic Fields  

Bibliography and Three Appendices  

Index  
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.