21. General Relativity - Wikibooks General relativity Introduction Introduction to Tensors General relativityMetric tensor Raising and Lowering Indices Geodesics Curvature http://en.wikibooks.org/wiki/General_relativity

General relativity From Wikibooks General relativity: Introduction Introduction to Tensors What is a tensor? Contravariant and Covariant Indices ... edit More advanced topics More on Tensors The Tensor Product Contraction Tensor Symmetries ... Authors Retrieved from " http://en.wikibooks.org/wiki/General_relativity Categories Science Views Module Discussion Edit this page History Personal tools Create an account or log in Navigation Main Page Community Portal Recent changes Random module ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 12:18, 5 December 2004. Content is available under GNU Free Documentation License About Wikibooks

22. Lecture Notes On General Relativity Sean M. Carroll's lecture notes from a onesemester graduate-level course he taught at MIT in 1996. Notes are in postscript format. http://pancake.uchicago.edu/~carroll/notes/

Lecture Notes on General Relativity Sean M. Carroll (gravitational waves disturbing a black hole, from NCSA This set of lecture notes on general relativity has been expanded into a textbook, Spacetime and Geometry: An Introduction to General Relativity , available for purchase online or at finer bookstores everywhere. About 50% of the book is completely new; I've also polished and improved many of the explanations, and made the organization more flexible and user-friendly. The notes as they are will always be here for free. These lecture notes are a lightly edited version of the ones I handed out while teaching Physics 8.962, the graduate course in General Relativity at MIT , during Spring 1996. Each of the chapters is available here as uncompressed postscript, but see next paragraph. (Need a postscript previewer ?) Constructive comments and general flattery may be sent to me via the address below. Dates refer to the last nontrivial modification of the corresponding file (fixing typos doesn't count). The notes as a whole are available as gr-qc/9712019 Other formats: if you don't like postscript, the notes are

23. Differential Gometry And General Relativity An introduction to differential geometry and general relativity by Stefan Waner at Hofstra. This is an upper level undergraduate mathematics course which assumes a knowledge of calculus and some linear algebra. http://people.hofstra.edu/faculty/Stefan_Waner/diff_geom/tc.html

Introduction to Differential Geometry and General Relativity Lecture Notes by Stefan Waner, Department of Mathematics, Hofstra University These notes are dedicated to the memory of Hanno Rund. TABLE OF CONTENTS 1. Preliminaries: Distance, Open Sets, Parametric Surfaces and Smooth Functions 2. Smooth Manifolds and Scalar Fields 3. Tangent Vectors and the Tangent Space 4. Contravariant and Covariant Vector Fields ... Download the latest version of the differential geometry/relativity notes in PDF format References and Suggested Further Reading (Listed in the rough order reflecting the degree to which they were used) Bernard F. Schutz, A First Course in General Relativity (Cambridge University Press, 1986) David Lovelock and Hanno Rund, Tensors, Differential Forms, and Variational Principles (Dover, 1989) Charles E. Weatherburn, An Introduction to Riemannian Geometry and the Tensor Calculus (Cambridge University Press, 1963) Charles W. Misner, Kip S. Thorne and John A. Wheeler, Gravitation (W.H. Freeman, 1973) Keith R. Symon

24. Modern Relativity Modernrelativity Special General Black Hole Mass Energy Einste A set of notes outlining general relativity and its applications, including modern theories of FTL travel and wormholes. http://www.geocities.com/zcphysicsms/

By David Waite Modern Relativity Message Board Chat Room These units explain general relativity only. We assume that the reader already has a full understanding of special relativity . For info on special relativity try our special relativity unit - Unit I - Special Relativity General Relativity Preface Unit II Foundations For General Relativity Chapter 4 Starting GR 4.1 - The Conceptual Premises For GR 4.2 - Tensors in GR 4.3 - The Metric and Invariants of GR ... 6.3 - Stress Energy of Matter and Einstein's Field Equations Unit III Using General Relativity Chapter 7 Electromagnetism in GR 7.1 - Maxwell's Equations 7.2 - Larmor Radiation and the Abraham-Lorentz Formulae Chapter 8 Robertson-Walker and the Big Bang ... 9.2 - Newtonian Limit Vs Gravitomagnetism Unit IV Black Holes Chapter 10 The Schwarzschild Black Hole 10.1 - The Schwarzschild Solution 10.2 - Hovering over a Schwarzschild Black Hole 10.3 - "Apparently" Lighter With Speed ... 11.2 - Hawking Radiation Unit V Fringe Physics in General Relativity Chapter 12 The New Frontiers 12.1 - Metric Engineering 12.2 - Wormholes 12.3 - Time Travel ... Appendix A : Newtonian-Relativistic Comparisons Appendix B : Planck - SI Unit Conversion Index Misc Affiliated Site Good Web Pages ... David's Martial Arts Site Email the author: WaiteDavid137@aol.com

25. SIMULATING GENERAL RELATIVITY Some examples of the phenomena of general relativity are simulated. This provides a graphical sight on the main general relativity concepts. The simulations include solutions in 3D (XY +time) and 4D (XYZ+time) spaces. http://www.raczynski.com/pn/genrel.htm

SIMULATING GENERAL RELATIVITY Stanislaw Raczynski stanracz@prodigy.net.mx ABSTRACT Some examples of the phenomena of general relativity are simulated. This provides a graphical and quite illustrative sight on the main general relativity concepts. The simulations include solutions in 3D (XY +time) and 4D (XYZ+time) spaces. The solutions are more general than those which can be obtained analytically. For example, the approach to the black hole is simulated not only as a radial particle movement, but as an arbitrary trajectory in the 3D space. The distortion of images of far objects seen through a neighborhood of a black hole is simulated using photon trajectories in 4D space. Also the entrance of an arbitrary trajectory into the horizon of the black hole is simulated both with the coordinate time (seen by the static observer) and with the proper time (clock) of the moving body. Time distortion at the neighborhood of the black hole is shown as a 3D “space-distortion” plot. Interesting simulation experiments are also shown for the rotating black hole. Click here to download the complete article Consult also: http://www.raczynski.com/pn/pn.htm

26. General Relativity Simulation Contest The purpose of this Contest is to prove general relativity using a (simple) algorithm. http://users.pandora.be/nicvroom/contest.htm

General Relativity Simulation Contest Description of Contest The purpose of this Contest is to prove General Relativity. The Contest consist of the following task: Write one general purpose program (any programming language will do) which simulates the movement of n objects over a certain period of time. The simulation method used (algorithms), should be based on the Rules of General Relativity. The program should be able to simulate and demonstrate the following examples: Forward movement (perihelion shift) of the planet Mercury (43 arc sec angle) around the Sun. The bending of light around the Sun (1.75 sec). The movement of a binary star system. The stars should spiral together. A clock in a space ship around the Earth. Twin paradox (SR). i.e. at least two clocks should be included. The behaviour of black holes. The results of the simulation should match actual observations. For the rules of General Relativity see the following: General Relativity with John Baez For the most elaborate list of links for General Relativity see: Relativity on the World Wide Web by Chris Hillman , maintained by John Baez For a technical discussion about the problems with numerical simulations regarding General Relativity see: Numerical Relativity If you want more about celestial mechanics simulations informal newsletter

27. General Relativity A laymen s guide to the theory of general relativity. http://archive.ncsa.uiuc.edu/Cyberia/NumRel/GenRelativity.html

Forward Back Up Map ... Information General Relativity Einstein's 1916 paper on General Relativity In 1916 Einstein expanded his Special Theory to include the effect of gravitation on the shape of space and the flow of time. This theory, referred to as the General Theory of Relativity , proposed that matter causes space to curve. JPEG Image Embedding Diagrams Picture a bowling ball on a stretched rubber sheet. GIF Image The large ball will cause a deformation in the sheet's surface. A baseball dropped onto the sheet will roll toward the bowling ball. Einstein theorized that smaller masses travel toward larger masses not because they are "attracted" by a mysterious force, but because the smaller objects travel through space that is warped by the larger object. Physicists illustrate this idea using embedding diagrams Contrary to appearances, an embedding diagram does not depict the three-dimensional "space" of our everyday experience. Rather it shows how a 2D slice through familiar 3D space is curved downwards when embedded in flattened hyperspace. We cannot fully envision this hyperspace; it contains seven dimensions, including one for time! Flattening it to 3D allows us to represent the curvature. Embedding diagrams can help us visualize the implications of Einstein's General Theory of Relativity. The Flow of Spacetime Another way of thinking of the curvature of spacetime was elegantly described by Hans von Baeyer. In a prize-winning

28. Unit 57 This site contains a comprehensive introduction to the basic ideas and tests of general relativity. http://astro.physics.sc.edu/selfpacedunits/Unit57.html

UNIT 57 THE GENERAL THEORY OF RELATIVITY Written for students in the USC Self-paced Astronomy courses NOTE: This Unit assumes you have studied Unit 56. The Learning Objectives and references are in the Self-Paced Study Guide Essay on the General Theory of Relativity by John L. Safko A. General Principle of Covariance (or Only the Tides are Real) Consider yourself in an elevator. You cannot see outside, so you must determine the nature of the surrounding universe by local experiments. You let go of a coin and it falls to the bottom of the elevator. Aha!, you say, I am at rest on Earth. But, you could be in a spaceship that is accelerating and far from any other object. This is shown in Fig. 57-1. Fig. 57-1: Locally being at rest on the Earth's surface is equivalent to being in a uniformly accelerated spaceship. Consider the opposite case. You float from the floor and the coin does not fall when you release it. Aha!, you say again, I am in space far from any other body. But, you could be freely falling towards the Earth as shown in Fig. 57-2. Fig. 57-2:

29. Sr Modern Relativity Modernrelativity Special Relativity Black Hole Mass Energy Special relativity is a special case of a more general physics. Once special relativity is understood, one may move on to a more general case of physics http://www.geocities.com/zcphysicsms/sr.htm

Special Relativity This Unit focuses on special relativity only. Special relativity is a special case of a more general physics. We use only Cartesian coordinate systems. In special relativity we do not consider gravitation, and it is also not a quantum theory. Thus many of the implications of special relativity that are often quoted as if they were general laws do not hold true in more general physics scenarios. Once special relativity is understood, one may move on to a more general case of physics known as general relativity For those that are ready for this step we have created a section on general relativity - Modern Relativity Special Relativity Preface Unit I Special Relativity Chapter 1 SR Made Simple 1.1 - Lorentz Coordinate Transformation 1.2 - Relative Space and Time 1.3 - Paradoxes ... 3.3 - Rotations, Rockets, and Frequency Shifts

30. A Quantum Leap For Cosmology (November 2001) - Physics World - PhysicsWeb A theory that unites quantum mechanics and general relativity claims that there was no first moment in time, but it still agrees with the predictions of classical cosmology. http://physicsweb.org/article/world/14/11/3

Advanced site search physics world sample issue Request a sample issue browse the archive January February March April May June July August September October November December Latest issue Subscribe to Physics World Media Information ... Editorial Staff quick search Search Physics World Physics World November 2001 A quantum leap for cosmology Physics in Action: November 2001 A theory that unites quantum mechanics and general relativity claims that there was no first moment in time, but it still agrees with the predictions of classical cosmology. It's in the stars One of the most challenging problems in modern physics is the application of quantum theory to the universe as a whole. Progress in this area has been plagued by two types of problem: conceptual and technical. The conceptual problems arise from the old difficulties of interpreting quantum theory. The standard interpretations require that the measuring instruments and observers are outside the quantum system described by the wavefunction. In the late 1950s, however, Hugh Everett proposed an interpretation of quantum theory that might apply to systems that include the observers and measuring instruments, but the adequacy of such interpretations has remained controversial to this day. The technical problems are no less severe or fundamental. Ever since the pioneering work of Bryce DeWitt, Charles Misner and others in the 1960s, quantum cosmology has basically been studied by applying quantum theory to simple models of the universe. These models typically assume that the universe is completely homogeneous. As a result they only have a few degrees of freedom - the radius of the universe and the value of one or more matter fields. One then makes a quantum-cosmological model by quantizing these simple descriptions of the universe.

31. [gr-qc/9911051] Complex Geometry Of Nature And General Relativity A paper by Giampiero Esposito attempting to give a selfcontained introduction to holomorphic ideas in general relativity. The main topics are complex manifolds, spinor and twistor methods, heaven spaces. http://arxiv.org/abs/gr-qc/9911051

General Relativity and Quantum Cosmology, abstract gr-qc/9911051 From: Esposito Giampiero [ view email ] Date: Mon, 15 Nov 1999 11:06:50 GMT (124kb) Complex Geometry of Nature and General Relativity Authors: Giampiero Esposito Categories: gr-qc Comments: 229 pages, plain Tex Report-no: DSF preprint 99/38 An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, spinor and twistor methods, heaven spaces. Full-text: PostScript PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv gr-qc find abs

32. GEOMETRY AND PHYSICS OF BRANES The SIGRAV Graduate School in Contemporary relativity and Gravitational Physics is held annually at the Centre for Scientific Culture Alessandro Volta , Villa Olmo, Como. It is primarily addressed to PhD students and young researchers in Physics and Mathematics who are interested in general relativity, astrophysics, experimental gravity and the quantum theories of gravitation. http://www.sissa.it/~bruzzo/sagp2001/sagp2001.html

4th SIGRAV GRADUATE SCHOOL ON CONTEMPORARY RELATIVITY AND GRAVITATIONAL PHYSICS and 2001 SCHOOL ON ALGEBRAIC GEOMETRY AND PHYSICS (SAGP2001) VILLA OLMO (COMO), 7-11 MAY 2001 GEOMETRY AND PHYSICS OF BRANES Supported by: SIGRAV (Italian Society for Gravitational Physics), National Research Project "Singularities, Integrability, Symmetries", SISSA (Trieste), University of Insubria (Como-Varese), Departmente of Chemistry, Physics and Mathematics of the University of Insubria at Como, Physics Department of the University of Milan, Physics Department of the University of Turin, Physics Department of the University of Rome "La Sapienza", Physics Department of the University of Rome "Tor Vergata", Physics Department of the University of Pavia. Download the first circular (Latex file) See the programme (PDF) The SIGRAV Graduate School in Contemporary Relativity and Gravitational Physics is held annually at the Centre for Scientific Culture "Alessandro Volta", Villa Olmo, Como. It is primarily addressed to PhD students and young researchers in Physics and Mathematics who are interested in general relativity, astrophysics, experimental gravity and the quantum theories of gravitation. In 2001 the School will be a joint venture with the School on Algebraic Geometry and Physics organized by the Mathematical Physics Group of the International School for Advanced Studies (SISSA) in Trieste. The School on Algebraic Geometry and Physics is part of a series of events that SISSA is organizing since 1996 aiming at fostering the interaction between mathematicians working in pure algebraic geometry and researchers who are interested in applications of algebraic geometry to physics, especially string theory and integrable systems. Information on the "Algebraic Geometry and Physics'' series is available from the web page

33. A Unified Field Theory A mathematical description of nature based on the geometry of SpaceTime. general relativity,Energy-Stress tensor, a set of current densities and Quantum mechanics for Spin 1 Bosons. Space-Time dimensions calculated and not put in by hand. http://homepage.ntlworld.com/peter.hickman1/

34. Physics And Astronomy Forums - General Relativity - General Physics Discussion But as the topic of this discussion is general relativity and as GR is exactly tht theory which disproves the Newtonian model, you should stop talking about http://www.physlink.com/Community/Forums/viewmessages.cfm?Forum=17&Topic=1064

35. "The Boundaries Of Nature: Special & General Relativity And Quantum Mechanics, A Big chunks of general relativity require only calculus if one starts with the metric And what does lie behind the formalism of general relativity? http://www.eftaylor.com/oersted/

"The Boundaries of Nature: Special & General Relativity and Quantum Mechanics, A Second Course in Physics:" Edwin F. Taylor's acceptance speech for the 1998 Oersted medal presented by the American Association of Physics Teachers, 6 January 1998 Edwin F. Taylor Center for Innovation in Learning, Carnegie Mellon University, Pittsburgh, PA 15213 (Now at 22 Hopkins Road, Arlington, MA 02476-8109, email eftaylor@mit.edu) ABSTRACT INTRODUCTION and fixed in me a determination to collaborate with him to develop and write up his insights for the world to enjoy. And, at one remove, John Wheeler's Ph.D. student Richard Feynman, whose thesis led to an introduction to quantum mechanics which now, fifty years later, we can exploit for the benefit of the modern student. These leaders in physics education have much in common: a fascination with the deep structure of Nature, enthusiasm for envisioning this structure in bold new ways, and absolute integrity in presenting both their vision and their own perplexities to an interested audience. All of us can join this enterprise without reservation or restraint, eliminating the need for anyone to express humility, false or otherwise. Here is the plan for this talk: First a brief look at general relativity and quantum mechanics, primarily to highlight how these subjects can be presented with no mathematical formalism beyond calculus. Second, some remarks on the proposed course and its potential benefits for various audiences and for the physics major. Finally, an inspirational conclusion.

36. Untitled Document A list of FAQs (Frequently Asked Questions) regarding Cosmology, String theory, relativity and general Physics http://www.het.brown.edu/people/watson/pages/resources.htm

Resources Below you will find links and suggested reading on various topics and at the beginning of each section a list of FAQ's (Frequently Asked Questions) that I have either received from others or that I have pondered at some point myself. If you would like to submit a question please do so [ here Topics Suggestions welcome General Physics Superstring Theory Cosmology ... General Relativity General Physics FAQs Can Theoretical Physics explain paranormal phenomena? Answer courtesy: Nobel Laureate Gerald t'Hooft What if all things can't be explained using physics? This is certainly a possibility, however, if physics and mathematics is inadequate to describe reality, that only leaves a realm that would be useless for us to know anyway. Besides "to know" means to apply a logical system to describe something, if mathematics (logic) is not applicable what else would one use? Faith is not an alternative to logic, for it is based on logic. One could define faith as the group of prejudices established by one to avoid reason. What is theoretical physics?

37. Transition Radius Method A new way to look at general relativity modifies the Schwarzschild black hole solution to explain the pattern of quark masses, lepton masses, and fundamental boson energies. http://webpages.charter.net/mdhpage/trmpdf2.pdf

38. General Relativity Tutorial (John Baez) This is bunch of interconnected web pages that serve as an informal introduction to general relativity. The goal is to demystify general relativity and get http://math.ucr.edu/home/baez/gr/gr.html

The General Relativity Tutorial John Baez This is bunch of interconnected web pages that serve as an informal introduction to that beautiful and amazingly accurate theory of gravity called general relativity . The goal is to explain the basic equation in this theory - Einstein's equation - with a minimum of fuss and muss. You can begin by reading this: Short Course Outline Clicking on any of the underlined key concepts will then take you to the corresponding point in this more detailed: Long Course Outline In the long course outline, clicking on any underlined key concept will take you to a still more detailed exposition of that concept. A more formal presentation of this material can be found here: The Meaning of Einstein's Equation including some extra stuff, but leaving out many other things. Alternatively, you can dive right in and read the adventures of Oz and the Wizard This is the fun part! In these stories, the hapless peasant Oz learns general relativity from a grumpy but powerful wizard. But, unless you are already familiar with general relativity, to understand these adventures you will need to look at the other material from time to time. All this material originated on sci.physics. Much of it is written by Oz and me, but there are also substantial contributions by Ted Bunn, Ed Green, Keith Ramsay, Bruce Scott, Bronis Vidugiris, and Michael Weiss.

39. Lanczos Collection Site announces the availability of the Cornelius Lanczos Collected Published Papers with commentaries. Lanczos (18931974) was one of the twentieth century's most versatile and innovative physicists and mathematicians. His papers cover an array of disciplines including general relativity, quantum mechanics, scientific computation, applied mathematics and numerical analysis. http://www.physics.ncsu.edu/lanczos

Announcing the CORNELIUS LANCZOS COLLECTED PUBLISHED PAPERS WITH COMMENTARIES Published by North Carolina State University College of Physical and Mathematical Sciences and Department of Physics Raleigh, North Carolina 27695-8202 USA [1998] Library of Congress Catalog Card Number: 98-67928 ISBN (for the Collection of Volumes I-VI): 0-929493-01-X [See Web: www.physics.ncsu.edu/lanczos (View the Order Form Ordering Instructions Collection 24 September 2002) (All orders are now being shipped from Raleigh, North Carolina) Cornelius Lanczos (1893-1974) was a physicist and mathematician who had a profound impact on the foundations of twentieth century science. His papers cover a vast array of disciplines, including general relativity, quantum mechanics, scientific computation, applied mathematics and numerical analysis. This Collection provides documentation (a) that Lanczos was indeed one of the twentieth century's most versatile and innovative scientific minds, and (b) that many of Lanczos's ideas are still of interest to present-day research in physics and applied mathematics. This Collection will be of special interest to theoretical physicists, numerical analysts and science historians. The Cornelius Lanczos Collected Published Papers with Commentaries (Lanczos Collection or CLCPPC herein-after referred to as the Collection) represents the second phase of a two-part celebration of the life and work of Cornelius Lanczos. The first phase of this celebration occurred in December 1993 when North Carolina State University's College of Physical and Mathematical Sciences hosted the Cornelius Lanczos International Centenary Conference. [See the

40. Douglas N. Arnold Director, Institute for Mathematics and its Applications. Numerical analysis, partial differential equations, mechanics; the numerical solution of the equations of general relativity. Publications, talks, teaching material, other resources. http://www.ima.umn.edu/~arnold/

Douglas N. Arnold Since 2001 I have held the position of Director of the Institute for Mathematics and its Applications in Minneapolis and Professor of Mathematics at the University of Minnesota. My research mostly concerns numerical analysis, partial differential equations, mechanics, and in particular, the interplay between these fields. Recently much of my effort has been directed toward the numerical solution of the equations of general relativity. Contact information Biographical sketch Curriculum vitae Research interests ... publications , and talks Educational material and information on students Graphics for the calculus classroom Graphics for complex analysis ... Photos Last modified January 1, 2003 by Douglas N. Arnold, domain='ima.umn.edu'; document.write('arnold@'); document.write('ima.umn.edu'); arnold(at)ima.umn.edu

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