FREE SPACETIME AND GEOMETRY: AN
INTRODUCTION TO GENERAL RELATIVITY PDF
Sean M. Carroll,John E. Neely,Richard R. Kibbe | 513 pages | 28 Sep 2003 | Pearson Education (US) | 9780805387322 | English | New Jersey, United States
Spacetime and Geometry:
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Special Relativity and Flat Spacetime. The Schwarzchild Solution.
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These lecture notes are a Spacetime and Geometry: An Introduction to General Relativity edited version of the ones I handed out while teaching Physics 8. Each of the chapters is available here as PDF. Constructive comments and general flattery may be sent to me via the address below.
What is even more amazing, the notes have been translated into French by Jacques Fric. Je ne parle pas francais, mais cette traduction devrait etre bonne.
Note that, unlike the book, no real effort has been made to fix errata in these notes, so be sure to check your equations. In a hurry? While you are here check out the Spacetime and Geometry page — including the annotated bibilography of technical and popular Spacetime and Geometry: An Introduction to General Relativity, many available for purchase online.
Special Relativity and Flat Spacetime 22 Nov ; 37 pages the spacetime interval — the metric — Lorentz transformations — spacetime diagrams
— vectors — the tangent space — dual vectors — tensors — tensor products — the Levi-Civita tensor — index manipulation —
electromagnetism — differential forms — Hodge duality — worldlines — proper time — energy-momentum vector — energy-momentum tensor
— perfect fluids — energy-momentum conservation.
Manifolds 22 Nov ; 24 pages examples — non-examples — maps — continuity — the chain rule — open sets — charts and atlases — manifolds
— examples of charts — differentiation — vectors as derivatives — coordinate bases — the tensor transformation law — partial derivatives are not tensors — the metric again — canonical form of the metric — Riemann normal coordinates — tensor densities — volume forms and integration.
Curvature 23 Nov ; 42 pages covariant derivatives and connections — connection coefficients — transformation properties — the Christoffel connection — structures on manifolds — parallel transport — the parallel propagator — geodesics — affine parameters — the exponential map
— the Riemann curvature tensor — symmetries of the Riemann tensor — the Bianchi identity — Ricci and Einstein tensors — Weyl tensor — simple examples — geodesic deviation — tetrads and non-coordinate bases — the spin connection — Maurer-Cartan structure equations — fiber bundles and gauge transformations.
More Geometry 26 Nov ; 13 pages pullbacks and pushforwards — diffeomorphisms — integral curves — Lie derivatives — the energy- momentum tensor one more time — isometries and Killing vectors. Weak Fields and Gravitational Radiation 26 Nov ; 22 pages the weak-field limit defined — gauge transformations — linearized Einstein equations — gravitational plane waves — transverse traceless gauge — polarizations
— gravitational radiation by sources — energy loss.
Skip to content This set of Spacetime and Geometry: An Introduction to General Relativity notes on general relativity has been expanded into a textbook, Spacetime and Geometry: An Introduction to General Relativityavailable for purchase online or at finer bookstores everywhere.
The notes as they are will always be here for free. Lecture Notes 1. Special Relativity and Flat Spacetime 22 Nov ; 37 pages the spacetime interval — the metric — Lorentz transformations — spacetime diagrams — vectors — the tangent space — dual vectors — tensors — tensor products — the Levi-Civita tensor — index manipulation — electromagnetism — differential forms — Hodge duality — worldlines — proper time — energy-momentum vector — energy-momentum tensor — perfect fluids — energy-momentum conservation 2.
Manifolds 22 Nov ; 24 pages examples — non-examples — maps — continuity — the chain rule — open sets — charts and atlases — manifolds
— examples of charts — differentiation — vectors as derivatives — coordinate bases — the tensor transformation law — partial derivatives are not tensors — the metric again — canonical form of the metric — Riemann normal coordinates — tensor densities — volume forms and integration 3. Curvature 23 Nov ; 42 pages covariant derivatives and connections — connection coefficients Spacetime and Geometry: An Introduction to General Relativity transformation properties — the Christoffel connection — structures on manifolds — parallel transport — the parallel propagator — geodesics — affine parameters — the exponential map — the Riemann curvature tensor — symmetries of the Riemann tensor — the Bianchi identity — Ricci and Einstein tensors — Weyl tensor — simple examples — geodesic deviation — tetrads and non- coordinate bases — the spin connection — Maurer-Cartan structure equations — fiber bundles and gauge transformations 4.
More Geometry 26 Nov ; 13 pages pullbacks and pushforwards — diffeomorphisms — integral curves — Lie derivatives — the energy- momentum tensor one more time — isometries and Killing vectors 6. Weak Fields and Gravitational Radiation 26 Nov ; 22 pages the weak-field limit defined — gauge transformations — linearized Einstein equations — gravitational Spacetime and Geometry: An Introduction to General Relativity waves — transverse traceless gauge — polarizations — gravitational radiation by sources — energy loss 7.
Phys B - General Relativity
Mayer Hall Monday and Wednesday, Grinstein Mayer Hall Office hours will continue until the earlier of 4pm or all students leaving Additional office hours will be arranged upon request. From the UCSD course catalogue: This is a two-quarter course on gravitation and the general theory of relativity. The first quarter is intended to be offered every year and Spacetime and Geometry: An Introduction to General Relativity be taken independently of the second quarter.
The second quarter will be offered in alternate years. Topics covered in the first quarter include special relativity, differential geometry, the equivalence principle, the Einstein field equations, and experimental and observational tests of gravitation theories.
The second quarter will focus on more advanced topics, including gravitational collapse, Schwarzschild and Kerr geometries, black holes, gravitational radiation, cosmology, and quantum gravitation. Due March??. Download detailed instructions. Zip file with students projects Notes Course notes prepared by the instructor. At students' request I have scanned my lecture notes. Be advised that they are written for my own use, so they tend to have scratches and corrections and marginal notes that may be irrelevant!
If anyone wants to transfer them to LaTeX please get in touch with the instructor. You may also want to use your favorite search engine to look for General Relativity Lecture Notes. Review of elements of differential geometry. Maps between manifolds, pull-back, push forward.
Derivatives without Spacetime and Geometry: An Introduction to General Relativity exterior and Lie. Isometries, Killing Vectors.
Minkowski space as an excuse to learn about causal structure and Penrose diagrams. Causality out of order. Anti de Sitter space. Homogeneous and Isotropic Spaces.
FRW metric. Friedmann Equations. Distance measurements; Age of Universe. Schwarzschild Metric. Birkhoff's Theorem. Red Shift. Kruskal coordinates and extension. Penrose Diagrams. More General Black Holes. Charged Holes. Spinning Holes. Penrose Process, Hawking Temperature.
Grinstein is a Theoretical Physicist. His main research interests are in the areas of particle physics and cosmology. Learn more about his recent work on his website. UCSD Library record. About this Spacetime and Geometry: An Introduction to General Relativity Practical Information.
Grinstein Mayer Hall Office hours will continue until the earlier of 4pm or all students leaving Additional office hours will be arranged upon request Course Description From the UCSD course catalogue: This is a two-quarter course on gravitation and the general theory of relativity.
Homework and Exams And Solutions. Zip file with students projects. Notes Course notes prepared by the instructor. Chapter 1: Mathematical review Review of elements of differential geometry. Chapter 2: Maximally symmetric spaces Generalities. Chapter 6: Other topics?? Tetrads, spinors, etc. Singularity theorems. Hawking radiation. Textbooks on Reserve There are many texts on General Relativity. You can read for free some that can be viewed on-line: go to the Roger on the UCSD library web page, and search for "General Relativity" or the like and select
"Electronic materials.
Here are some hardcopy texts that I have placed on Reserve at Geisel Library. Robert M. Wald General Relativity. Anthony Zee Einstein gravity in a nutshell. Sean Carroll Spacetime and geometry: an introduction to general relativity. Charles W. Misner, Kip S. Thorne, John Archibald Wheeler Gravitation. Bernard F. Benjamin Grinstein Distinguished Professor of Physics. Contact The Team Of course, students know how to contact "the team" anyway.
General Relativity Robert M. Gravitation Charles W.
