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Topic: Mathematics of general relativity

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  Spartanburg SC | GoUpstate.com | Spartanburg Herald-Journal   (Site not responding. Last check: 2007-10-22)
The principle of general covariance states that the laws of physics should take the same mathematical form in all reference frames and was one of the central principles in the development of general relativity.
Measurements in physics are performed in a relatively small region of spacetime and this is one reason for studying the local structure of spacetime in general relativity, whereas determining the global spacetime structure is important, especially in cosmological problems.
In the general relativity literature, it is conventional to use the component syntax for tensors.
www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=mathematics_of_general_relativity   (4077 words)

  General relativity - Wikipedia, the free encyclopedia
In general relativity, phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as free-fall, orbital motion, and spacecraft trajectories) are taken in general relativity to represent inertial motion in a curved spacetime.
General relativity is incompatible with quantum mechanics; it is generally held that one of the most important unsolved problems in modern physics is the problem of obtaining a true quantum theory of gravitation.
General relativity was developed by Einstein in a process that began in 1907 with the publication of an article on the influence of gravity and acceleration on the behavior of light in special relativity.
en.wikipedia.org /wiki/General_relativity   (4504 words)

 Mathematics of general relativity - Wikipedia, the free encyclopedia
The mathematics of general relativity refers to various mathematical structures and techniques that are used in Albert Einstein's theory of general relativity.
The principle of general covariance states that the laws of physics should take the same mathematical form in all reference frames and was one of the central principles in the development of general relativity.
Measurements in physics are performed in a relatively small region of spacetime and this is one reason for studying the local structure of spacetime in general relativity, whereas determining the global spacetime structure is important, especially in cosmological problems.
en.wikipedia.org /wiki/Mathematics_of_general_relativity   (3786 words)

 General Relativity
When "generalized" to include gravitation, the equations of relativity predict that gravity, or the curvature of spacetime by matter, not only stretches or shrinks distances (depending on their direction with respect to the gravitational field) but also w ill appear to slow down or "dilate" the flow of time.
In the decade after its publication in 1916, Einstein's Theory of General Relativity led to a burst of experimental activity in which many of its predictions were vindicated.
These predictions were encapsulated in a series of field equations that laid the foundation for all subsequent research into relativity and partly for modern cosmology as well.
archive.ncsa.uiuc.edu /Cyberia/NumRel/GenRelativity.html   (683 words)

 ScienceDaily: Loop quantum gravity   (Site not responding. Last check: 2007-10-22)
Mathematically, spin networks are related to group representation theory and can be used to construct knot invariants such as the Jones polynomial.
Since classical general relativity can be formulated as a BF theory with constraints, scientists hope that a consistent quantization of gravity may arise from the perturbation theory of BF spin-foam models.
General covariance, also known as diffeomorphism invariance, is the invariance of physical laws under arbitrary coordinate transformations.
www.sciencedaily.com /encyclopedia/loop_quantum_gravity   (2679 words)

 ipedia.com: Loop quantum gravity Article   (Site not responding. Last check: 2007-10-22)
General relativity is the theory of gravitation published by Albert Einstein in 1915.
Mathematically LQG is local gauge theory of the self-dual subgroup of the complexified Lorentz group, which is related to the action of the Lorentz group on Weyl spinors commonly used in elementary particle physics.
General covariance (also known as diffeomorphism invariance) is the invariance of physical laws (for example, the equations of general relativity) under arbitrary coordinate transformations.
www.ipedia.com /loop_quantum_gravity.html   (6274 words)

 NOVA | Einstein's Big Idea | Relativity (Lightman Essay) | PBS
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.
Many of the predictions of general relativity, such as the bending of starlight by gravity and a tiny shift in the orbit of the planet Mercury, have been quantitatively confirmed by experiment.
General relativity may be the biggest leap of the scientific imagination in history.
www.pbs.org /wgbh/nova/einstein/relativity   (1248 words)

 Relativity, Gravitation, and Cosmology: A Basic Introduction (Oxford Master Series in Physics) by Ta-Pei Cheng, ISBN: ...   (Site not responding. Last check: 2007-10-22)
There are plenty of graduate textbooks on general relativity, points out Cheng (physics, U. of Missouri), and plenty of popular works describing in for lay readers.
Students are expected to have the usual mathematics at the calculus level, some familiarity with matrices, and the physics of mechanics and electromagnetism including differential equations of Maxwell's theory.
Mathematical accessibility, together with the various pedagogical devices (e.g., worked-out solutions of chapter-end problems), make it practical for interested readers to use the book to study general relativity and cosmology on their own.
www.campusi.com /isbn_0198529562.htm   (667 words)

 General relativity: Introduction - Wikibooks, collection of open-content textbooks
General relativity is an extension to the idea of special relativity in order to handle gravity.
While the mathematics behind general relativity can be daunting, the basic idea behind general relativity is quite simple.
While the mathematical details can be complex, the basic idea is that the effects of gravity are equivalent to the effects of acceleration on an observer.
en.wikibooks.org /wiki/General_relativity:_Introduction   (732 words)

 Relativity Tutorial
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".
In general, given any two events A and B with B inside the future light cone of A, there is one unaccelerated worldline connecting A and B, just as there is one straight line connecting two points in space.
Relativity also leads to interesting objects such as fl holes, but these are not very relevant to cosmology.
www.astro.ucla.edu /~wright/relatvty.htm   (3935 words)

 Einstein, Friedmann and Relativity
This became known as the general theory of relativity and is a theory of gravity, the key long-range force in the Universe.
General relativity can account for the observed precession of the perihelion of Mercury about the Sun and the observed difference in hydrogen maser clocks in satellites orbiting Earth compared with those on the ground.
General relativity is not just on interest to astrophysicists and gravitational wave physicists.
outreach.atnf.csiro.au /education/senior/cosmicengine/einstein.html   (1301 words)

 General Relativity. (from Mathematics and Physical Sciences) --  Encyclopædia Britannica
Although Einstein's general theory of relativity is generally accepted, physicists have suggested other possible theories of gravitation.
Thus, relativity is concerned with measurements made by different observers moving relative to one another.
Mathematics is often defined as the study of quantity, magnitude, and relations of numbers or symbols.
www.britannica.com /eb/article-92650   (670 words)

The key to understanding general relativity (at least in the mathematical sense) comes from partial dirivative equations.
Coceptually the physical foundations of General Relativity are given from what is known as the Einstein Tensor G (for simplicity one can think of it as the gravitational tensor).
About: This document is meant to be a very brief introduction into some of the mathematics used within general relativity, it is in no way meant to be a complete treatise on the subject.
members.tripod.com /da_theoretical1/grtensors/genrel01.htm   (1044 words)

 Aether, Relativity and Superfluidity - Barry C. Mingst
General Relativity is a relativistic theory of gravity.
The first postulate of General Relativity is that the source of the gravitational field is the stress-energy tensor of a perfect fluid, T {sections 4.6 & 4.7, A first course in general relativity, Schutz}.
General Relativity distinguishes gravity from all other forces because "all bodies given the same initial velocity follow the same trajectory in a gravitational field, regardless of their internal composition" {ibid, p121}.
www.mountainman.com.au /aether_3.html   (3139 words)

 General Theory of Relativity
Mathematics can at best be made to describe some of the workings of nature.
The mathematics of general relativity is like a secret religion in which the plebs are not able to understand anything, but must obey the priests.
Nature cannot do mathematics, she can work through the geometry of a situation and she can perform vector addition at a point (because this is fundamentally geometric).
users.powernet.co.uk /bearsoft/GnRel.html   (905 words)

 Trafford Publishing: The Mathematics of Relativity for the Rest of Us   (Site not responding. Last check: 2007-10-22)
The Mathematics of Relativity for the Rest of Us is intended to give the generally educated reader a thorough and factual understanding of Einstein's theory of relativity - including the difficult mathematical concepts, even if the reader is not trained in higher mathematics.
The relativity of time, space, and mass is covered first, giving some attention to the history of the two main divisions of relativity, the special and the general.
Once special relativity and its mathematics are established, general relativity is covered, beginning with its relationship to Newton's laws and advancing through its revolutionary concepts as well as its mathematics.
www.trafford.com /4dcgi/robots/00-0233.html   (1064 words)

 [No title]
The invariant interval of flat space-time is generalized to that of curved space-times, and leads to an understanding of the basic properties of simple cosmological models and of the collapse of a star to form a fl hole.
The foundation needed in addition in order to understand the mathematics of general relativity is an understanding of the calculus of several variables.
The overall branch of mathematics needed for a full study of general relativity is called either Riemannian geometry of differential geometry.
www.edu-observatory.org /eo/bkr/bkr.91.08   (777 words)

 3quarksdaily: Monday Musing: General Relativity, Very Plainly
Before I do that, however, a caveat: the mathematics of general relativity is very advanced and well beyond my own rather basic knowledge.
Indeed, Einstein himself needed help from professional mathematicians in formulating some of it, and well after general relativity was published (in 1915) some of the greatest mathematicians of the twentieth century (such as Kurt Gödel) continued to work on its mathematics, clarifying and providing stronger foundations for it.
This is the principle of equivalence, and it is the heart of general relativity.
3quarksdaily.blogs.com /3quarksdaily/2005/09/general_relativ.html   (3644 words)

So, in 1895, Hilbert was appointed to the chair of mathematics at the University of Göttingen, where he continued to teach for the rest of his career.
Hilbert's eminent position in the world of mathematics after 1900 meant that other institutions would have liked to tempt him to leave Göttingen and, in 1902, the University of Berlin offered Hilbert Fuchs' chair.
In the analysis of mathematical talent one has to differentiate between the ability to create new concepts that generate new types of thought structures and the gift for sensing deeper connections and underlying unity.
www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Hilbert.html   (1587 words)

 Abraham Taub
Searching for a consistent formulation of Mach's principle in general relativity, he investigated, for the case of spatially homogeneous Ricci-flat spacetimes, the general solutions of Killing's equation for each of the nine types of transitive three-parameter continuous groups discussed by Bianchi.
Among his achievements were the first development of Hamilton's principle for a perfect fluid and other variational principles in general relativistic hydrodynamics, the circulation theorem, the relativistic Rankine-Hugoniot equations, and the stability of fluid motions in general relativity [5].
Taub was a professor of mathematics at Berkeley from 1964 until his retirement, in 1978.
www.siam.org /siamnews/09-01/taub.htm   (1455 words)

 Amazon.com: General Relativity: Books: I. R. Kenyon   (Site not responding. Last check: 2007-10-22)
Einstein's general theory of relativity is perhaps the most important perspective to emerge in a century of astonishing progress in the field of physics.
curvature and the Schwarzschild metric, tests of the theory of relativity, fl holes and their properties, gravitational radiation and methods for its detection, the impact of general relativity on cosmology, and the continuing search for a quantum theory of gravity.
The general theory of relativity proposed by Einstein in 1915 imposed a new view of the space-time we inhabit: instead of matter moving through a passive space-time continuum the general theory of relativity (GR) asserts that the presence of matter should distort space-time.
www.amazon.com /exec/obidos/tg/detail/-/0198519966?v=glance   (550 words)

 Analog models of General Relativity: Talks   (Site not responding. Last check: 2007-10-22)
In many ways the main issue was whether condensed matter and/or optical systems could be used to mimic aspects of general relativity; and what the prospects are for medium-term/short-term experimental implementation of these analog systems.
Analog models of general relativity are useful probes of Hawking radiation: Because the short-distance physics is explicitly known (atomic physics), the cutoff is physically understood---this helps clarify the role of trans-Planckian frequencies in general relativity fl holes, which in these condensed-matter analogs are replaced by "trans-Bohrian" physics.
The term ``q-gravity'' (short for quasi-gravity) is to be understood here as referring to theories involving mathematical entities, and in particular a spacetime metric, analogous to but qualitatively different from the corresponding genuinely gravitation structures.
www.physics.wustl.edu /~visser/Analog/talks.html   (2418 words)

General relativity is usually written with lots of superscripts and subscripts.
This tutorial is no substitute for reading books on general relativity and doing the exercises - just like dipping your toe in the ocean is no substitute for learning to swim.
It concentrates on the mathematics of general relativity and other gauge fields, such as Maxwell's equations and the Yang-Mills equations, which describe the strong and electroweak forces.
math.ucr.edu /home/baez/gr/gr.html   (751 words)

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