1. General Relativity - Wikipedia, The Free Encyclopedia general relativity (GR) or General theory of relativity (GTR) is the geometrical theory of gravitation published by Albert Einstein in 1915/16. http://en.wikipedia.org/wiki/General_relativity

General relativity From Wikipedia, the free encyclopedia Jump to: navigation search For a generally accessible and less technical introduction to the topic, see Introduction to general relativity A simulated Black Hole of ten solar masses as seen from a distance of 600 km with the Milky Way in the background (horizontal camera opening angle: 90°). General relativity GR ) or General theory of relativity GTR ) is the geometric theory of gravitation published by Albert Einstein in 1915/16. It unifies special relativity Newton's law of universal gravitation , and the insight that gravitational acceleration can be described by the curvature of space and time , this latter being produced by the mass energy and momentum content of the matter in spacetime General relativity is distinguished from other metric theories of gravitation by its use of the Einstein field equations to relate spacetime content and spacetime curvature. The field equations are a system of partial differential equations whose solution gives the metric tensor of spacetime, describing its "shape". In the resulting geometry, an object moving inertially in a gravitational field is viewed as following a geodesic path that may be found using the Christoffel symbols of the metric.

2. General Relativity This is a basic postulate of the Theory of general relativity. It states that a uniform gravitational field (like that near the Earth) is equivalent to a 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

3. General Relativity 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. http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/General_relativity.html

General relativity Mathematical Physics index History Topics Index Version for printing 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.

4. Gr Highly recommendable collection of interconnected web pages that serve as an informal introduction to general relativity. While some mathematics is used, http://math.ucr.edu/home/baez/gr/

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. If you want, you can dive right in and read the adventures of Oz and the Wizard This is the fun part! In these tales, the hapless peasant Oz learns general relativity from a grumpy but powerful wizard. But, unless you are already familiar with general relativity, to follow these adventures you'll need to look at other material from time to time, like 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 When you're here, clicking on any underlined key concept takes you to a still more detailed exposition of that concept. A more formal presentation of all this material can be found here: The Meaning of Einstein's Equation including some extra stuff, but leaving out many other things.

5. NOVA | Einstein's Big Idea | Relativity (Lightman Essay) | PBS Learn about Einstein s general relativity and how the theory might help to describe the nature of the universe. Article describes how his work helped other http://www.pbs.org/wgbh/nova/einstein/relativity/

var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www."); document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E")); Relativity and the Cosmos by Alan Lightman Einstein's Big Idea homepage 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 250 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 from 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. The essence of gravity 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 "yardstick." Published in 1915, general relativity proposed that gravity, as well as motion, can affect the intervals of time and of space. The key idea of general relativity, called the equivalence principle, is that gravity pulling in one direction is completely equivalent to an acceleration in the opposite direction. A car accelerating forwards feels just like sideways gravity pushing you back against your seat. An elevator accelerating upwards feels just like gravity pushing you into the floor.

6. Unit 57 Overview of the basic ideas and principal applications of general relativity. Written by John L. Safko for students in the selfpaced astronomy courses at 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:

7. Section C General Relativity: MT 2003 Lecture notes and problem sheets for a course taught by NMJ Woodhouse at Oxford University in 2003. http://www.maths.ox.ac.uk/~nwoodh/gr/index.html

General Relativity, MT 2003 Lecture notes Lectures 1-16 Revised 23.12.03 Problem sheets Sheet 1 Sheet 2 Sheet 3 Sheet 4 ... N.M.J. Woodhouse Michaelmas Term 2003 nwoodh@maths.ox.ac.uk

8. General Relativity This metric is the basis of the three classic tests of Einstein s theory of general relativity 1) the perihelion advance of Mercury, 2) the bending of http://www.physics.fsu.edu/Courses/Spring98/AST3033/Relativity/GeneralRelativity

Introduction to General Relativity Problems with Newtonian Gravity Newton was fully aware of the conceptual difficulties of his action-at-a-distance theory of gravity. In a letter to Richard Bentley Newton wrote: It is inconceivable, that inanimate brute matter should, without the mediation of something else, which is not material, operate upon, and affect other matter without mutual contact; as it must do, if gravitation, ...., be essential and inherent in it. And this is one reason, why I desired you would not ascribe innate gravity to me. That gravity should be innate, inherent, and essential to matter, so that one body may act upon another, at a distance through vacuum, without the mediation of anything else, by and through their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it." So, clearly, Newton believed that something had to convey gravitational influence from one body to another. When later it became clear that influences travel at finite speeds it was reasonable to suppose this true of gravity also. But Newton's law of gravity did not incorporate the finite travel time of gravitational influences. If right now the sun were to be destroyed by a passing black hole we would not feel the gravitational effects until about 8 minutes had elapsed. Because Newton's law did not include such retardation effects, and permitted violations of special relativity, it was clear that Newton's law had to be an approximation to the correct law of gravity.

9. Differential Gometry And General Relativity Online introduction to differential geometry and general relativity. This is an upper level undergraduate mathematics course which assumes a knowledge of http://people.hofstra.edu/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

10. General Relativity -- From Eric Weisstein's World Of Physics The fundamental principle of general relativity asserts that accelerated reference frames and reference frames in gravitation fields are equivalent. http://scienceworld.wolfram.com/physics/GeneralRelativity.html

Modern Physics Relativity Theory General Relativity Miscellaneous General Relativity General Relativity A theory invented by Albert Einstein which describes gravitational forces in terms of the curvature in space caused by the presence of mass. The fundamental principle of general relativity asserts that accelerated reference frames and reference frames in gravitation fields are equivalent. General relativity states that clocks run slower in strong gravitational fields (or highly accelerated frames), predicting a gravitational redshift . It also predicts the existence of gravitational lensing gravitational waves gravitomagnetism , the Lense-Thirring effect , and relativistic precession of orbiting bodies. Bardeen-Petterson Effect Bertotti-Robinson Solution Black Hole Black Hole No Hair Theorem ... Schwarzschild Black Hole Adler, R.; Bazin, M.; and Schiffer, M. Introduction to General Relativity, 2nd ed. New York: McGraw-Hill, 1975. Anderson, J. L. Principles of Relativity Physics. New York: Academic Press, 1967. Bergmann, P. G.

11. Modern Relativity Set of notes outlining general relativity and its applications, including cosmology and gravitational waves, but also fringe physics topics such as 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. General Relativity Founded by Subrahmanyan Chandrasekhar, the general relativity group at the University of Chicago engages in research across a wide variety of topics in http://physics.uchicago.edu/t_rel.html

Research Classes Events People ... Physics Home ON THIS PAGE: Robert P. Geroch Robert M. Wald General Relativity Founded by Subrahmanyan Chandrasekhar , the General Relativity group at the University of Chicago engages in research across a wide variety of topics in classical and quantum gravitation, as well as forays into astrophysics, condensed matter theory, and mathematical physics. This work is carried out within the interdisciplinary Enrico Fermi Institute . Some topics of long-standing interest include black holes, quantum field theory in curved spacetime, cosmology, and functional analysis. Robert P. Geroch Ph.D., Princeton, 1967. Professor, Dept. of Physics, Enrico Fermi Institute, Committee on Conceptual Foundations of Science , and the College. Theoretical physics, general relativity. Asymptotic Structure of Space-time. R. Geroch. In Asymptotic Structure of Space-time, eds. T.P. Esposito and L. Witten, Plenum Press, 1977. General Relativity from A to B. R. Geroch. University of Chicago Press, 1978. Distorted Black Holes. R. Geroch and J.B. Hartle. J. Math. Phys.

13. General Relativity According to the principle of equivalence from general relativity, any frequency shift which can be shown to arise from acceleration of a radiating source http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html

Gravitational Red Shift According to the principle of equivalence from general relativity, any frequency shift which can be shown to arise from acceleration of a radiating source could also be produced by the appropriate gravitational field. Thus the expected shift in radiation frequency in a gravitational field can be related to the relativistic doppler shift experienced from an accelerating light source. Gravity and the photon Applications: Harvard tower experiment Index General relativity ideas HyperPhysics ... Relativity R Nave Go Back Harvard Tower Experiment In just 22.6 meters, the fractional gravitational red shift given by is just 4.92 x 10 , but the Mossbauer effect with the 14.4 keV gamma ray from iron-57 has a high enough resolution to detect that difference. In the early 60's physicists Pound, Rebka,and Snyder at the Jefferson Physical Laboratory at Harvard measured the shift to within 1% of the predicted shift. By just using the expression for gravitational potential energy near the Earth, and using the m in the relativistic energy expression , the gain in energy for a photon which falls distance h is Comparing the energy shifts on the upward and downward paths gives a predicted difference The measured difference was The success of this experiment owed much to the care of Pound and Rebka in preparing the source. They electroplated cobalt-57 onto the surface of a thin sheet of iron and then heated the combination at 1220 K for an hour. The heat treatment caused the cobalt to diffuse into the iron to a depth of about 300 nm or 1000 atomic spacings. The source was then mounted on the cone of a loudspeaker driven at 10Hz to sweep the source velocity in a sinusoidal variation. The detector was a thin sheet of iron about 14 micrometers thick which was also annealed. The heat treatments were found to be crucial in obtaining high resolution.

14. Lecture Notes On General Relativity - S. Carroll These notes represent approximately one semester s worth of lectures on introductory general relativity for beginning graduate students in physics. http://nedwww.ipac.caltech.edu/level5/March01/Carroll3/Carroll_contents.html

The notes as a whole are available as gr-qc/9712019 Lecture Notes on General Relativity Sean M. Carroll Enrico Fermi Institute University of Chicago , 5460 S. Ellis Ave., Chicago, IL 60637 December 1997 Abstract. These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications: gravitational radiation, black holes, and cosmology. Individual chapters, and potentially updated versions, can be found at http://pancake.uchicago.edu/~carroll/notes/ Table of Contents TABLE OF CONTENTS PREFACE BIBLIOGRAPHY SPECIAL RELATIVITY AND FLAT SPACETIME ... COSMOLOGY For a postscript version of the article, click here

15. SpringerLink Home - Main www.kluweronline.com/issn/00017701/contents - Similar pages general relativityHowever the magnitude of the effect predicted by the Newtonian analysis differs from the magnitude predicted by general relativity by a factor of 2. http://www.kluweronline.com/issn/0001-7701/contents

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16. Lecture Notes On General Relativity This set of lecture notes on general relativity has been expanded into a textbook, Spacetime and Geometry An Introduction to general relativity, http://preposterousuniverse.com/grnotes/

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

17. SpringerLink Home - Main www.springerlink.com/openurl. asp?genre=journal issn=00017701 - general relativity and related topics are published (in advance of publication in conventional http://www.springerlink.com/openurl.asp?genre=journal&issn=0001-7701

18. [gr-qc/9712019] Lecture Notes On General Relativity xxx.lanl.gov/abs/grqc/9712019 - Similar pages general relativity and Gravitation SocietyThe International Society on general relativity and Gravitation was formed in 1971 and is the successor to the International Committee on general relativity http://xxx.lanl.gov/abs/gr-qc/9712019

lanl.arXiv.org gr-qc Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Full-text links: Download: PostScript PDF Other formats Citations SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted) NASA ADS CiteBase p revious ... ext General Relativity and Quantum Cosmology Title: Lecture Notes on General Relativity Authors: Sean M. Carroll (Submitted on 3 Dec 1997) Abstract: These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications: gravitational radiation, black holes, and cosmology. Comments: 238 pages, numerous figures. Individual chapters, and potentially updated versions, can be found at this http URL Subjects: General Relativity and Quantum Cosmology (gr-qc) ; Astrophysics (astro-ph); High Energy Physics - Theory (hep-th) Report number: NSF-ITP/97-147 Cite as: arXiv:gr-qc/9712019v1 Submission history From: Sean Carroll [ view email Wed, 3 Dec 1997 02:39:44 GMT (277kb)

19. General Relativity general relativity What does the General Theory of Relativity tell us about space, time, and existence? The profound effects of this revolutionary theory! http://www.allaboutscience.org/general-relativity-faq.htm

General Relativity You are here: Science Learn More about the Theory of Relativity! General Relativity What is General Relativity? General relativity is also referred to as "The General Theory of Relativity." It was initially presented in a paper by Albert Einstein in 1915. Its primary thrust was to add the effects of gravity to "The Special Theory of Relativity," making special relativity a special case of general relativity. In the same way, ten years earlier, Einstein proposed The Theory of Special Relativity with the primary thrust of eliminating the concept of a fixed reference frame in favor of relative inertial frames in conjunction with the newly learned fact that the speed of light was a constant when measured in any inertial reference frame. This theory, in a similar way, makes the Newtonian Euclidian geometry of space a special case of special relativity. So rather than these new theories refuting the old theories, they actually verified that the previous theories were special cases of a more complicated theory that explains more of reality. Many of us who have studied physics remember an equation that states that force equals mass times acceleration (f = ma) for a mass being accelerated by a constant force. We also remember how strange it was that an almost identical equation, force equals mass times the gravitational acceleration constant (f = mg) was used to determine the weight of a non-accelerating object in a gravitational field. This similarity (or relationship) between "a" and "g" forms the conceptual basis for general relativity.

20. General Relativity Einstein s general theory of relativity is principally concerned with the largescale effects of gravitation, unlike the special theory which is mainly http://www.neutron.anl.gov/hyper-physics/rgeneral.html

General Theory of Relativity relativity (rèl´e-tîv¹î-tê), physical theory, introduced by Albert Einstein , that discards the concept of absolute motion and instead treats only relative motion between two systems or frames of reference. Space and time are no longer viewed as separate, independent entities but rather as forming a four-dimensional continuum called space-time Einstein's general theory of relativity is principally concerned with the large-scale effects of gravitation , unlike the special theory which is mainly applicable in small-scale systems and quantum mechanics. The general theory recognizes the equivalence of gravitational and inertial mass , and asserts that material bodies produce the curvature of the space-time continuum and that the path of a body is determined by this curvature. The theory predicts that a ray of light is deflected by a gravitational field; observations of starlight passing near the sun, first made by Arthur Eddington and colleagues during a 1919 eclipse of the sun, confirmed this. The theory also predicts a red shift of spectral lines of substances in a gravitational field, a result confirmed by observation of light from white dwarf stars. Finally, the theory also accounts for the entire observed perihelion motion of the planet Mercury, only part of which could be explained by Newtonian celestial mechanics. Reconciling the theory with quantum mechanics in a unified field theory has proven difficult. Superstring theory may be able to link quantum gravitation (the study of quantum fields in a curved space-time) with the other quantum theories.

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