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Kay, D.C., Schaum s Outline of Tensor Calculus, McGraw-Hill, New York, 1988. Good to use to learn about differential geometry. Lightman, A.P., Press, W.H., Price, R.H., and Teukolsky, S.A., Problem Book in Relativity and Gravitation, Princeton University Press, Princeton, New Jersey, 1975. Lots of solved relativity problems, but light on discussion. Ludvigsen, M., General Relativity: A Geometric Approach, Cambridge University Press, Cambridge, 1999. A really nice but slim volume. Good to read after you have mastered some of the others. Misner, C., Thorne, K., and Wheeler, J., Gravitation, Freeman, San Francisco, 1973. Certainly the most comprehensive book out there. Everything you need to master, the subject can be found here. This is a good place to read about the Cartan methods. Peebles, P.J.E., Principles of Physical Cosmology, Princeton University Press, Princeton, New Jersey, 1993. Schutz, B.F., A First Course in Relativity, Cambridge University Press, Cambridge, 1985. A nice book that provides a gentle introduction to the subject. I like the fact that it discusses one forms and how they are introduced. Good book to get started. Stephani, H., Relativity: An Introduction to Special and General Relativity, 3d ed., Cambridge University Press, Cambridge, 2004. Taylor, E.F., and Wheeler, J.A., Exploring Black Holes: An Introduction to General Relativity, Addison-Wesley, San Francisco, 2000.
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Papers and Web Sites
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We also relied on a few papers and Web sites. The papers referenced were downloaded online, so we are providing the Web references. Alcubierre, M., The Warp Drive: Hyper-Fast Travel Within General Relativity. arXiv:gr-qc/0009013 v1 5 Sep 2000. Available at: http://arxiv.org/PS cache/ gr-qc/pdf/0009/0009013.pdf
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References and Bibliography
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Finley, D., Physics 570 Course Notes. Available at: http://panda.unm.edu/ courses/ nley/p570/handouts/connections.pdf The class where I rst learned relativity. Dr. Finley instilled my preference for using Cartan s equations and sparked my interest in null tetrads. In particular, you may nd the notes on connections useful. Goncalves, S.M.C.V Naked Singularities in Tolman-Bondi-de Sitter Collapse. ., Available at: http://xxx.lanl.gov/PS cache/gr-qc/pdf/0012/0012032.pdf Gutti, S., Gravitational Collapse of Inhomogeneous Dust in (2 + 1) Dimensions. Available at: http://lanl.arxiv.org/abs/gr-qc/0506100 Gutti, S., Singh, T.P., Sundararajan, P., and Vaz, C., Gravitational Collapse of an In nite Dust Cylinder. Living Reviews is a nice Web site we used to do research on uids and the stress-energy tensor. It has a lot of great information on relativity. http://relativity.livingreviews.org/ Wikipedia is a great resource but should be used with caution. They allow anyone to post, so there is no telling what s true and what s not. In any case, there are many great articles covering many topics, including relativity. Just be sure to double check what you nd. Two we used were http://en.wikipedia.org/wiki/Petrov classi cation http://en.wikipedia.org/wiki/Pp-wave spacetimes
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INDEX
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absolute derivative geodesics, 82 active gravitational mass, 123. See also Newtonian theory af ne connection, 65 af ne parameter, 82 anisotropic space, 256. See also isotropic space astigmatic, 313 basis coordinate basis, 29 one forms, 30, 94, 98 99 transformation, 32, 101 102 set holonomic basis, 94 vectors, 24, 29, 31, 94 differentiation, 64, 65 Bianchi identities, 87 Big Bang, 276 black hole, 224. See also special relativity classi cation, 230 coordinate singularities, 233 235 Eddington-Finkelstein coordinates, 236 239 Kruskal coordinates, 242 244 event horizon, 241 in nite redshift, 234 Kerr black hole, 233, 234, 244 245, 250 Boyer-Lindquist coordinates, 245 Cauchy horizon, 248, 249 cross terms, 245 ergosphere, 245 frame dragging, 249, 250
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horizons, 245 246 lense-thirring effect, 250 metric, 244 orbital equations, 251, 252 Penrose process, 245 reduced circumference, 251 singularity, 253 solution, 233 Reissner-Nordstr m, 233 Schwarzschild black hole coordinate singularities, 234 Eddington-Finkelstein coordinates, 236, 239 in nite redshift, 234 Kruskal coordinates, 242, 243 radially infalling particle, 238, 239 solution, 233 tortoise coordinate, 237, 239 Bondi metric, 32. See also metric Boyer-Lindquist coordinates, 240 Brinkmann metric, 195 Cartan s structure equation, 93 121, 139. See also curvature tensor bases transformation, 100 103 inverse matrix, 101 102 tetrad, 100 basis one forms, 98 100 commutation coef cients, 96 98 curvature tensor, 139 146 rst structure equation, 104, 207 holonomic bases, 94 95 basis vectors, 94
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