1. NCSA/LCA-Potsdam-WashU International Numerical Relativity Group Home Page phenomena predicted by Einstein's Theory of general relativity. Our WWW servers are for this server Numerical Relativity, general relativity, Einstein, Astrophysics, Black Holes http://jean-luc.ncsa.uiuc.edu/

Potsdam/Germany Mirror ] [Champaign/US Mirror] NCSA/LCA Potsdam WashU International Numerical Relativity Group Computing Resources for the AEI Numerical Relativity Group Welcome People Papers Projects Movies Exhibits Codes Our international group uses supercomputers to study black holes, gravitational waves, and other phenomena predicted by Einstein's Theory of General Relativity. Our WWW servers are an integral part of our research efforts. Our group is the result of a close collaboration between members of the Laboratory for Computational Astrophysics at the National Center for Supercomupting Applications in Champaign-Urbana Illinois, the Washington University Relativity Group in St. Louis Missouri, and the in Potsdam, Germany. Here you can find information on group projects, members, publications, collaborations, and much, much more. Enjoy our Server! Keywords for this server : Numerical Relativity, General Relativity, Einstein, Astrophysics, Black Holes, Gravitational Waves, Relativistic Hydrodynamics, Neutron Stars, Hyperbolic and Elliptic PDEs, Parallel Computing, Scientific Visualization. Search Astronomylinks for links: provided by astronomylinks.com

2. General Relativity Tutorial general relativity Tutorial. John Baez. This is bunch of interconnected web pages that serve as an informal introduction to general relativity. http://math.ucr.edu/home/baez/gr/gr.html

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 across the key ideas without big complicated calculations. You can begin by reading a Short Course Outline Clicking on any of the underlined key concepts will then take you to the corresponding point in a 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. Alternatively, you can begin to read some of the adventures of Oz and the Wizard However, 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. General relativity is usually written with lots of superscripts and subscripts. Mitchell Charity has kindly improved these web pages so that they look nice. However, not all web browsers can handle this.

3. Lecture Notes On General Relativity Lecture Notes on general relativity. Try the NoNonsense Introduction to general relativity, a 24-page condensation of the full-blown lecture notes. 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

4. Hyperspace GR Hypertext Dunsby s Internet GR course at Cape Town. The general relativity News Archives. general relativity and Quantum Cosmology Preprints. http://www.maths.qmw.ac.uk/hyperspace/

Welcome to HyperSpace! This service is sponsored by the International Society on General Relativity and Gravitation Welcome to the HyperSpace service at QMW, a set of hypertext based services for general relativity research provided by the QMW Relativity group, based on a similar service at the University of British Columbia. Software is by Steve Braham We have the following: Software for finding GR (e)mail addresses GR News Archive Our GR related FTP archives Preprint searches in the LANL archives ... Services of interest Address searches Here we have a nifty forms-based program, GR, that searches a list of e-mail and snail mail addresses important to the GR community. It has many personas that cross-reference each other in an intelligent way so that searching is made easy. It also gives links to various preprint databases. We have the following: GR the full forms-based program or you can access a simple version of each persona if you do not have forms support: GR/people Finds the e-mail and snail mail addresses of people in the GR community. GR/journal Finds the e-mail and snail mail addresses of journals and GR research groups.

5. Differential Gometry And General Relativity Online introduction to differential geometry and general relativity. Introduction to Differential Geometry and general relativity. 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

6. General Relativity Introduction to general relativity. Problems with Newtonian Gravity. Newton was fully aware of the conceptual difficulties of his actionat-a-distance theory of gravity. In a letter to Richard Bentley Newton wrote " the three classic tests of Einstein's theory of general relativity 1) the perihelion advance of Mercury, 2) the http://www.physics.fsu.edu/Courses/Spring98/AST3033/Relativity/GeneralRelativity

7. NOVA Online/Einstein Revealed/Relativity (Lightman Essay) Relativity and the Cosmos. by Alan Lightman. In November of 1919, at the age of 40, Albert Einstein became an overnight celebrity, thanks to a solar eclipse. theory of gravity, general relativity. general relativity was the first major What was general relativity? Einstein's earlier theory of time and space, Special Relativity, proposed http://www.pbs.org/wgbh/nova/einstein/relativity

Relativity and the Cosmos by Alan Lightman In November of 1919, at the age of 40, Albert Einstein became an overnight celebrity, thanks to a solar eclipse. An experiment had confirmed that light rays from distant stars were deflected by the gravity of the sun in just the amount he had predicted in his theory of gravity, General Relativity. General Relativity was the first major new theory of gravity since Isaac Newton's, more than two hundred and fifty years earlier. Einstein became a hero, and the myth building began. Headlines appeared in newspapers all over the world. On November 8, 1919, for example, the London Times had an article headlined: "The Revolution In Science/Einstein Versus Newton." Two days later, The New York Times' headlines read: "Lights All Askew In The Heavens/Men Of Science More Or Less Agog Over Results Of Eclipse Observations/Einstein Theory Triumphs." The planet was exhausted with World War I, eager for some sign of humankind's nobility, and suddenly here was a modest scientific genius, seemingly interested only in pure intellectual pursuits. What was General Relativity? Einstein's earlier theory of time and space, Special Relativity, proposed that distance and time are not absolute. The ticking rate of a clock depends on the motion of the observer of that clock; likewise for the length of a "yard stick." Published in 1915, General Relativity proposed that gravity, as well as motion, can affect the intervals of time and of space.

8. General Relativity general relativity. Mathematical Physics index. History Topics Index. general relativity is a theory of gravitation and to understand the background to the theory we have to look at how theories of http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/General_relativity.html

General relativity Mathematical Physics index History Topics Index General relativity is a theory of gravitation and to understand the background to the theory we have to look at how theories of gravitation developed. Aristotle 's notion of the motion of bodies impeded understanding of gravitation for a long time. He believed that force could only be applied by contact, force at a distance being impossible, and a constant force was required to maintain a body in uniform motion. Copernicus 's view of the solar system was important as it allowed sensible consideration of gravitation. Kepler 's laws of planetary motion and Galileo 's understanding of the motion and falling bodies set the scene for Newton 's theory of gravity which was presented in the Principia in 1687. Newton 's law of gravitation is expressed by F G M M d where F is the force between the bodies of masses M M and d is the distance between them. G is the universal gravitational constant. After receiving their definitive analytic form from Euler Newton 's axioms of motion were reworked by Lagrange Hamilton , and Jacobi into very powerful and general methods, which employed new analytic quantities, such as potential, related to force but remote from everyday experience.

9. Lecture Notes On General Relativity general relativity This homepage contains lecture notes on the course of general relativity FX2/H97 read in the fall semester 1997 at the Physics Institute of http://sunkl.asu.cas.cz/~had/gr.html

General Relativity This homepage contains lecture notes on the course of general relativity FX2/H97 read in the fall semester 1997 at the Physics Institute of NTNU, Trondheim. Some parts were added later. It is still under construction (see the dates of last revision of each chapter). Some viewers do not allow to see the PS-files on the screen. However, you can download it (using the 'save'-command) and print it on a PostScript printer. Contents: Introduction Special relativity Basic concepts of general relativity Spherically symmetric spacetimes ... References A supplementary text on lower level can be found in lecture notes on cosmology which was read in the fall semester 1999 as a part of another course. To get more information contact, please, the author. Readers may find interesting also other web-pages on general relativity referred at Hillman's list and Syracuse University list Petr Hadrava, Astronomical Institute of the Academy of Sciences of the Czech Republic, 251 65 Ondrejov, Czech Republic tlf.: +420 204 620 141

10. Modern Relativity Modernrelativity Special General Black Hole Mass Energy Einste For info on special relativity try our special relativity unit Unit I - Special Relativity. general relativity Preface. Foundations For general relativity. http://www.geocities.com/zcphysicsms/

By David Waite Modern Relativity David Waite's Special Relativity Lecture Tape (2 hours) 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

11. Unit 57 UNIT 57. THE GENERAL THEORY OF RELATIVITY. Written Only in the last few years has the experimental side of general relativity blossomed. We 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:

12. General Relativity general relativity. The final steps to the theory of general relativity were taken by Einstein and Hilbert at almost the same time. http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/General_relativity.html

General relativity Mathematical Physics index History Topics Index General relativity is a theory of gravitation and to understand the background to the theory we have to look at how theories of gravitation developed. Aristotle 's notion of the motion of bodies impeded understanding of gravitation for a long time. He believed that force could only be applied by contact, force at a distance being impossible, and a constant force was required to maintain a body in uniform motion. Copernicus 's view of the solar system was important as it allowed sensible consideration of gravitation. Kepler 's laws of planetary motion and Galileo 's understanding of the motion and falling bodies set the scene for Newton 's theory of gravity which was presented in the Principia in 1687. Newton 's law of gravitation is expressed by F G M M d where F is the force between the bodies of masses M M and d is the distance between them. G is the universal gravitational constant. After receiving their definitive analytic form from Euler Newton 's axioms of motion were reworked by Lagrange Hamilton , and Jacobi into very powerful and general methods, which employed new analytic quantities, such as potential, related to force but remote from everyday experience.

13. 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

14. Relativity On The World Wide Web The purpose of these pages is to promote the appreciation, understanding, and applications of special and general relativity. Here http://math.ucr.edu/home/baez/relativity.html

Relativity on the World Wide Web Original by Chris Hillman; maintained by John Baez The evolving event horizon during the axisymmetric merger of two equal mass black holes (simulation by the Binary Black Hole Grand Challenge Alliance) Welcome! The purpose of these pages is to promote the appreciation and understanding of the special and general theories of relativity by providing links to on-line scientifically accurate educational resources aimed at a variety of audiences, including popular science sites (places to go if you don't want to see any scary math), visualization sites , (places to go if you just want to see some truly fabulous pictures with some genuine scientific content), web tutorials on relativity theory (just the thing if you're not yet sure you want to really buckle down and study this stuff), observational and experimental evidence bearing on relativity theory, including fantastically beautiful astronomical images, a discussion of some specific scientifically inaccurate claims about cosmology and general relativity, formal coursework, including full length lecture notes (

15. PhysicsWeb - A Quantum Leap For Cosmology 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 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 Previous Physics World November 2001 Next 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.

16. Australasian Society For General Relativity And Gravitation Australasian Society for general relativity and Gravitation. general relativity, Gravitation and Cosmology WWW sites worldwide. Other http://www.physics.adelaide.edu.au/ASGRG/

Australasian Society for General Relativity and Gravitation Contents Membership information Newsletters Job vacancies Committee / contact information ... Other links worldwide The Australasian Society for General Relativity and Gravitation (ASGRG) was formed at a meeting of mathematicians and physicists in Canberra in September 1994. The Society aims to bring together researchers who work in a wide range of areas within mathematical, theoretical and experimental gravitation: exact solutions of general relativity, mathematical relativity, numerical relativity, quantum gravity, cosmology, estimation of the gravitational wave signals produced by astronomical sources, and development of techniques and technology for detecting these signals with earth- and satellite-based antennae. It was decided to form the society to facilitate discussion of mutual problems of interest and to provide greater cooperation to solve the outstanding problems in the various fields. We see our role as providing a regional forum in Australia and New Zealand similar to the recently formed Topical Interest Group in Gravitation of the American Physical Society, and the international GRG society. The official name and constitution of the Society were adopted at the first General Meeting, which was held during the

17. General Relativity general relativity. Einstein s 1916 paper on general relativity. In This is a basic postulate of the Theory of general relativity. It 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

18. [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: [ view email ] Date: Mon, 15 Nov 1999 11:06:50 GMT (124kb) Complex Geometry of Nature and General Relativity Author: Giampiero Esposito 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

19. 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

20. Numerical Relativity Exhibitions These are WWW exhibits based on the NCSA Relativity Group's work and on general relativity. Exhibits about calculations, computers, virtual reality, and the history of science. http://jean-luc.ncsa.uiuc.edu/Exhibits/

Numerical Relativity Exhibitions These are WWW exhibits based on the NCSA Relativity Group's work and on General Relativity. Here you will find exhibits about calculations, computers, virtual reality, the history of science, and much more. Spacetime Wrinkles an extensive exhibit on Einstein and numerical relativity. Schwarzschild Worm Hole An embedding diagram of a single black hole obtained from a numerical solution of the Einstein equations that describe the behavior of the gravitational field. Visualizing Black Hole Spacetimes Stills from a movie of a distorted black hole evolution. Interaction of a Gravitational Wave with a Black Hole A simulation of the interaction of a gravitational wave and a black hole. Model of an Expanding (Closed) Universe This is a visualization of a 2-dimensional model of the 3-dimensional universe. NCSA Relativity Group Exhibits Page / jean-luc@aei-potsdam.mpg.de June 2001

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