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 41. General Relativity/What Is A Tensor? - Wikimedia Labs, Collection Oct 9, 2007 At this point, you should get some sense as to why tensors are important in general relativity. General relativity is all about matterhttp://en.labs.wikimedia.org/wiki/General_relativity/What_is_a_tensor?

42. Academia.edu | People Who Have General Relativity As A Research Interest (76)
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43. Wapedia - Wiki: Congruence (general Relativity)
May 24, 2010 In general relativity, a congruence (more properly, a congruence of curves) is the set of integral curves of a (nowhere vanishing) vector
http://wapedia.mobi/en/Congruence_(general_relativity)
Wiki: Congruence (general relativity) In general relativity , a congruence (more properly, a congruence of curves ) is the set of integral curves of a (nowhere vanishing) vector field in a four-dimensional Lorentzian manifold which is interpreted physically as a model of spacetime . Often this manifold will be taken to be an exact or approximate solution to the Einstein field equation Contents:
1. Types of congruences

2. Relation with vector fields

3. Physical interpretation

4. Kinematical description
...
5. References
1. Types of congruences
Congruences generated by nowhere vanishing timelike, null, or spacelike vector fields are called timelike null , or spacelike respectively. A congruence is called a geodesic congruence if the tangent vector field has vanishing covariant derivative
2. Relation with vector fields
The integral curves of the vector field are a family of non-intersecting parameterized curves which fill up the spacetime. The congruence consists of the curves themselves, without reference to a particular parameterization. Many distinct vector fields can give rise to the same congruence of curves, since if

 44. Black Hole Duality: General Relativity Without Singularities Oct 29, 2010 In one description, an observer falls freely through empty space, in another one , she hits a surface smack on, yet both descriptions arehttp://www.science20.com/alpha_meme/black_hole_duality_general_relativity_withou

45. General Relativity
Expo/Science Industry/Spacetime Wrinkles Forward Back Up Map Glossary Information General Relativity. Einstein's 1916 paper on General Relativity
http://archive.ncsa.illinois.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

46. Relativity Tutorial
Tutorial by Ned Wright (UCLA) featuring a stepby-step introduction to special relativity (focusing on spacetime diagrams) and the basic ideas of general relativity.
http://www.astro.ucla.edu/~wright/relatvty.htm
Galilean Relativity
Relativity can be described using space-time diagrams . Contrary to popular opinion, Einstein did not invent relativity. Galileo preceded him. Aristotle had proposed that moving objects (on the Earth) had a natural tendency to slow down and stop. This is shown in the space-time diagram below.
Note the curved worldline above. This shows a variable velocity, or an acceleration . Galileo objected to Aristotle's hypothesis, and asked what happened to an object moving on a moving ship.
Now it is still moving in its final state. Galileo proposed that it is only relative velocities that matter. Thus a space-time diagram can be transformed by painting it on the side of a deck of cards, and then skewing the deck to one side but keeping the edges along a straight line:
Straight worldlines (unaccelerated particles) remain straight in this process. Thus Newton's First Law is preserved, and non-accelerated worldlines are special. This Galilean transformation does not affect the time. Thus two observers moving with respect to each other can still agree on the time, and thus the distance between two objects, which is the difference in their positions measured at equal times, can be defined. This allowed Newton to describe an inverse square law for gravity. But Galilean transformations do not preserve velocity. Thus the statement "The speed limit is 70 mph" does not make sense but don't try this in court. According to relativity, this must be re-expressed as "The magnitude of the relative velocity between your car and the pavement must be less than 70 mph". Relative velocities are OK.

47. NOVA | Einstein's Big Idea | Relativity (Lightman Essay) | PBS
General relativity may be the biggest leap of the scientific imagination in history. Unlike many previous scientific breakthroughs, such as the principle of natural selection, or
http://www.pbs.org/wgbh/nova/einstein/relativity/
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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.

49. Physics Virtual Bookshelf: Relativity
A collection of articles about relativity
http://www.upscale.utoronto.ca/GeneralInterest/Relativity.html
 Relativity The listings are in roughly the order in which these topics might be taught. Topic Description Author Format Special Theory of Relativity: html pdf The Special Relativity document by Professor Key that is the next listing largely concentrates on the effects predicted by the theory, such as time dilation, length contraction, etc. This document is considerably longer than Professor Key's, and tends to concentrate more on the worldview suggested by the theory. (157k/310k) David M. Harrison html and pdf Special Theory of Relativity A discussion of the postulates of special relativity and their consequences, from a first year physics course that uses minimal mathematics; the entire set of materials from the course is available by clicking here Anthony W. Key html Inertial Frames of Reference html pdf A brief summary of the concept of Inertial Frames of Reference in Newtonian and Einsteinian Physics. (25k/35k) David M. Harrison

50. The Field Equations
This was not clear when Einstein first developed general relativity, but it was pointed out in one of the very first published critiques of Einstein's 1916 paper, and
http://www.mathpages.com/rr/s5-08/5-08.htm
5.8� The Field Equations
You told us how an almost churchlike atmosphere is pervading your desolate house now. And justifiably so, for unusual divine powers are at work in there. ����������������������������������������������������������������������������������������������� Besso to Einstein, 30 Oct 1915 The basis of Einstein's general theory of relativity is the audacious idea that not only do the metrical relations of spacetime deviate from perfect Euclidean flatness, but that the metric itself is a dynamical object.� In every other field theory the equations describe the behavior of a physical field, such as the electric or magnetic field, within a constant and immutable arena of space and time, but the field equations of general relativity describe the behavior of space and time themselves.� The spacetime metric is the field.� This fact is so familiar that we may be inclined to simply accept it without reflecting on how ambitious it is, and how miraculous it is that such a theory is even possible, not to mention (somewhat) comprehensible.� Spacetime plays a dual role in this theory, because it constitutes both the dynamical object and the context within which the dynamics are defined.� This self-referential aspect gives general relativity certain characteristics different from any other field theory.� For example, in other theories we formulate a Cauchy initial value problem by specifying the condition of the field everywhere at a given instant, and then use the field equations to determine the future evolution of the field.� In contrast, because of the inherent self-referential quality of the metrical field, we are not free to specify arbitrary initial conditions, but only conditions that already satisfy certain self-consistency requirements (a system of differential relations called the Bianchi identities) imposed by the field equations themselves.

51. Relativity
Provides information on the history, experiments and paradoxes of relativity.
http://nobelprize.org/physics/educational/relativity/

52. 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!
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.

 53. General-relativity | Define General-relativity At Dictionary.com –noun Physics . See under relativity ( def. 2http://dictionary.reference.com/browse/general-relativity

54. Theory: Special Relativity (SLAC VVC)
A brief overview of the theory of special relativity, and how it pertains to particles at SLAC (Stanford Linear Accelerator)
http://www2.slac.stanford.edu/vvc/theory/relativity.html
Virtual Visitor Center at SLAC
• Main Topics Home Accelerator Detectors Experiments ... Theory Interactive Areas EGS FGST LAT document.write('')
Special Relativity
Newton's laws of motion give us a complete description of the behavior moving objects at low speeds. The laws are different at speeds reached by the particles at SLAC. Einstein's Special Theory of Relativity describes the motion of particles moving at close to the speed of light. In fact, it gives the correct laws of motion for any particle. This doesn't mean Newton was wrong, his equations are contained within the relativistic equations. Newton's "laws" provide a very good approximate form, valid when v is much less than c . For particles moving at slow speeds (very much less than the speed of light), the differences between Einstein's laws of motion and those derived by Newton are tiny. That's why relativity doesn't play a large role in everyday life. Einstein's theory supersedes Newton's, but Newton's theory provides a very good approximation for objects moving at everyday speeds. Einstein's theory is now very well established as the correct description of motion of relativistic objects, that is those traveling at a significant fraction of the speed of light.

55. General Relativity Tutorial
Highly recommendable collection of interconnected web pages that serve as an informal introduction to general relativity. While some mathematics is used, the focus is on the
http://math.ucr.edu/home/baez/gr/gr.html
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.

56. Understanding General Relativity Too
Stepby-step introduction to general relativity, from the basic principles via a heuristic account of the mathematics of curved spaces to the Einstein field equations, plus
http://www.rafimoor.com/english/GRE.htm
 Home English Hebrew Understanding General Relativity too Table of Content Understanding General Relativity too By Rafi Moor The purpose of this article is to introduce General Relativity to people with basic knowledge of mathematics and physics. Familiarity with the basics of Special Relativity is also required. Talking about General Relativity without getting into higher mathematics is not an easy mission. Much of the theory of GR deals with advanced mathematical issues. One can't cover the main topics of GR without getting into some mathematical issues. I have divided the article to three parts so that the reader can decide how deep he wants to dive into the subject. The first part introduces the principles of GR without any mathematics at all. The second part discusses curved space geometry without getting into the detailed mathematics of it. The third part describes Einstein's field equation and some consequences of it.

57. HowStuffWorks "How Special Relativity Works"
The major principles of special relativity (SR) are discussed in an accessible way, via 5 segments, to help you understand the lingo and theories involved.
http://www.howstuffworks.com/relativity.htm
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How Special Relativity Works
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• Introduction to How Special Relativity Works 1.0 - The Fundamental Properties of the Universe Mass and Energy Light ... See all Everyday Myths articles
• Physics: Einstein's Equation and Fission
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Pages from Albert Einstein's original manuscript in which he defines his theory of relativity If you are a fan of science fiction, then you know that "relativity" is a fairly common part of the genre. For example, people on Star Trek are always talking about the space-time continuum, worm holes, time dilations and all sorts of other things that are based on the principle of relativity in one way or another. If you are a fan of science you know that relativity plays a big part there as well, especially when talking about things like black holes and astrophysics. If you have ever wanted to understand the fundamentals of relativity, then this edition of

58. General Relativity - An Overview Of Einstein's Theory Of General Relativity
Einstein's Theory of General Relativity expands on the initial concepts of relativity to create a geometric framework of spacetime which can be used to explain gravity
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Einstein's Theory of General Relativity
By Andrew Zimmerman Jones , About.com Guide
zSB(3,3) (Continued from Page 3) In Albert Einstein's 1905 theory ( special relativity ), he showed that among inertial frames of reference there was no "preferred" frame. The development of general relativity came about, in part, as an attempt to show that this was true among non-inertial (i.e. accelerating) frames of reference as well.
Evolution of General Relativity
In 1907, Einstein published his first article on gravitational effects on light under special relativity. In this paper, Einstein outlined his "equivalence principle," which stated that observing an experiment on the Earth (with gravitational acceleration g ) would be identical to observing an experiment in a rocket ship that moved at a speed of g . The equivalence principle can be formulated as: we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system.

59. Edwin F. Taylor - General Relativity
Free sample chapters available for download purchase by phone 1800-282-0693 (int'l 1-201-767-5021) purchase by fax
http://www.eftaylor.com/general.html
General Relativity
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Exploring Black Holes
Introduction to General Relativity

Edwin F. Taylor and
John Archibald Wheeler

Addison Wesley Longman HELP with the second edition of Exploring Black Holes Albert Einstein told us that a star or other massive object distorts spacetime in its vicinity. Sufficient distortion makes it impossible to describe matter and motion with the single "inertial reference frame" used in Newton's theory of mechanics and Einstein's theory of special relativity. General relativity describes the distortion of spacetime near a star, white dwarf, neutron star, or black hole and predicts the resulting motion of stones, satellites, and light flashes. Learning general relativity usually requires mastering Einstein's field equations, which are expressed in the complicated mathematics of tensors or differential forms. But big chunks of general relativity require only calculus if one starts with the metric describing spacetime around Earth or black hole. Expressions for energy and angular momentum follow, along with predictions for the motions of particles and light. Students study the Global Positioning system, precession of Mercury's orbit, gravitational red shift, orbits of light and deflection of light by Sun, frame-dragging and precession near a rotating body, gravitational waves, and two different models of the Universe.

60. Notes On Special Relativity
A standard introduction to special relativity where explanations are based on pictures called spacetime diagrams.
http://www.phys.vt.edu/~takeuchi/relativity/notes
College of Science Physics Dept Tatsu Takeuchi Special Relativity > Lecture Notes
Special Relativity Lecture Notes