81. General Relativity In The Global Positioning System effects of GR on GPSCategory Science Physics relativity Articles......general relativity in the global positioning system. Neil Ashby Universityof Colorado n_ashby@mobek.colorado.edu. The Global Position http://www.phys.lsu.edu/mog/mog9/node9.html

General relativity in the global positioning system Neil Ashby University of Colorado n_ashby@mobek.colorado.edu The Global Position System (GPS) consists of 24 earth-orbiting satellites, each carrying accurate, stable atomic clocks. Four satellites are in each of six different orbital planes, of inclination 55 degrees with respect to earth's equator. Orbital periods are 12 hours (sidereal), so that the apparent position of a satellite against the background of stars repeats in 12 hours. Clock-driven transmitters send out synchronous time signals, tagged with the position and time of the transmission event, so that a receiver near the earth can determine its position and time by decoding navigation messages from four satellites to find the transmission event coordinates, and then solving four simultaneous one-way signal propagation equations. Conversely, gamma-ray detectors on the satellites could determine the space-time coordinates of a nuclear event by measuring signal arrival times and solving four one-way propagation delay equations. Apart possibly from high-energy accelerators, there are no other engineering systems in existence today in which both special and general relativity have so many applications. The system is based on the principle of the constancy of c in a local inertial frame: the Earth-Centered Inertial or ECI frame. Time dilation of moving clocks is significant for clocks in the satellites as well as clocks at rest on earth. The weak principle of equivalence finds expression in the presence of several sources of large gravitational frequency shifts. Also, because the earth and its satellites are in free fall, gravitational frequency shifts arising from the tidal potentials of the moon and sun are only a few parts in

82. [physics/9908041] Gravitational Waves: An Introduction This paper presents an elementary introduction to the theory of gravitational waves. This article is meant for students who have had an exposure to general relativity, but results from general relativity have been derived in the appendices. http://xxx.lanl.gov/abs/physics/9908041

Physics, abstract physics/9908041 Gravitational Waves: An Introduction Authors: Indrajit Chakrabarty Comments: Lecture notes presenting an elementary introduction to the theory of gravitational waves. To be submitted to Resonance, Journal of Science Education with a lesser mathematical content. For later revisions, see this http URL Subj-class: Physics Education; Popular Physics In this article, I present an elementary introduction to the theory of gravitational waves. This article is meant for students who have had an exposure to general relativity, but, results from general relativity used in the main discussion have been derived and discussed in the appendices. The weak gravitational field approximation is first considered and the linearized Einstein's equations are obtained. We discuss the plane wave solutions to these equations and consider the transverse-traceless (TT) gauge. We then discuss the motion of test particles in the presence of a gravitational wave and their polarization. The method of Green's functions is applied to obtain the solutions to the linearized field equations in presence of a nonrelativistic, isolated source. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Links to: arXiv physics find abs

83. General Relativity Introduction to general relativity. Problems with Newtonian Gravity.Newton Thus was born the general theory of relativity. Einstein's 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.

84. The 5D Space-Time-Matter Consortium We are a group of physicists and astronomers working on a 5dimensional version of general relativity. http://astro.uwaterloo.ca/~wesson/#PUB

This page is maintained by Sanjeev Seahra Last modified: February 01, 2002

85. General Relativity ) general relativity (and a treatment of tensors). To visit that site, click hereto enter the TrekZone. Astrophysical Implications of general relativity. http://www.home.gil.com.au/~praxis/gr/

Hi there! This page is dedicated to my favourite area of physics. Here you will find heaps of mathematical derivations and info on General Relativity (GR), astrophysical implications of GR, data on planets of the Solar System, and comments on all things astrophysical. Although there will be quite a bit of text, this page is meant to be more of a mathematical source of information. As a final note, this page is under construction. In fact, you'll probably find sections with no info! I get to update this page a few times a year, so come back once in a while. :) General Relativity (and a treatment of tensors) This section of my site on deals with Albert Einstein's General Theory of Relativity. This section is continuing to expand as I learn more new and interesting things about GR. I get to do most of my reading in the summer holidays, so you can propably expect this section to get updated about once a year. Please note that this site is still under construction, so some of the links won't work yet! This section is meant to be an online reference to General Relativity, providing a 'no frills' approach. It is more of a summary, with derivations of just about every single equation included. By "summary," I mean that I do not go into detail explaining every single step. I assume, for example, that the reader fully understands the Einstein summation convention, and is familiar with any references made to Special Relativity. But don't let this warning scare you! Read on - there are things which will interest even the most casual reader.

86. Special And General Relativity - New Mathematical Formulations Presentation of new mathematical formulations for both the Special and general Theories of relativity.Category Science Physics relativity Alternative......Mathematical knowledge required is no greater than undergraduate level.SPECIAL AND general relativity NEW MATHEMATICAL FORMULATIONS. http://www.relativitydomains.com/

SPECIAL AND GENERAL RELATIVITY - NEW MATHEMATICAL FORMULATIONS The purpose of this site is the presentation of new, simplified mathematical formulations of Albert Einstein's Special and General Theories of Relativity. The content is therefore of a technical nature, requiring a good working knowledge of mathematics and applied mechanics, up to graduate level. The current literature on these theories primarily works with such techniques as Riemannian Geometry and the Tensor Calculus etc., and while these are extremely powerful mathematical tools, they are also very complex. Therefore, when applied to Einstein's two most well known theories, they result in a formulation quite difficult to follow for even the most accomplished post graduate student. In the presentations here, nothing more complex than first and second order differential equations of functions of a complex variable are used to develop both theories from first principles.The first paper should be reviewed first because it is the simpler of the two, and because the paper on the General Theory assumes a familiarity with the application of the above techniques to these subjects. The links below connect with short introductory pages to each paper and to links to the sections of the papers themselves.

87. General Relativity Group Homepage The general relativity Group consists of four members of the Applied MathematicsGroup, together with a number of postdoctoral research assistants and Ph.D http://www.maths.soton.ac.uk/applied/relativity/

Applied Homepage GR Homepage People Research ... Links The General Relativity Group consists of four members of the Applied Mathematics Group , together with a number of postdoctoral research assistants and Ph.D students. At Southampton the major thrust of investigation is the classical theory and its application to astrophysics. The major emphasis of the group is in the increasingly important area of numerical relativity. Other topics studied include singularities and black holes, causality violation, asymptotic structure, cosmic strings, cosmology, pulsating black holes and neutron stars, instabilities in rotating stars, gravitational wave sources and the classification of metrics using algebraic computing. The general relativity group hosted the first British Gravity Meeting in March, 2001. For an overview of general relativity please visit our new GR Explorer site.

88. Lecture Notes On General Relativity Download lecture notes on special relativity, general relativity, differential geometry, and spherically symmetric spacetimes in postscript format. 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

89. Gravitation And The General Theory Of Relativity general relativity. The general Theory of relativity Tests of the Theoryof general relativity. general relativity and Newton's gravitational http://csep10.phys.utk.edu/astr162/lect/cosmology/gravity.html

Gravitation and the General Theory of Relativity As we have discussed in an earlier section , the theoretical physicist Albert Einstein introduced his Special Theory of Relativity in 1905 and his General Theory of Relativity in 1915. The first showed that Newton's Three Laws of Motion were only approximately correct, breaking down when velocities approached that of light. The second showed that Newton's Law of Gravitation was also only approximately correct, breaking down when gravitation becames very strong. Special Relativity Einstein's Special Theory of Relativity is valid for systems that are not accelerating. Since from Newton's second law an acceleration implies a force, special relativity is valid only when no forces act. Thus, it cannot be used generally when there is a gravitational field present (as we shall see below in conjunction with the Principle of Equivalence, it can be used over a sufficiently localized region of spacetime). We have already discussed some of the important implications of the Special Theory of Relativity. For example, the most famous is probably the relationship between mass and energy . Other striking consequences are associated with the dependence of space and time on velocity: at speeds near that of light, space itself becomes contracted in the direction of motion and the passage of time slows. Although these seem bizarre ideas (because our everyday experience typically does not include speeds near that of light), many experiments indicate that the Special Theory of Relativity is correct and our "common sense" (and Newton's laws) are incorrect near the speed of light.

90. Differential Gometry And General Relativity A course from the Department of Mathematics at Hofstra University on differential geometry and general relativity. http://www.hofstra.edu/~matscw/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

91. General Relativity ON THIS PAGE Sean M. Carroll Robert P. Geroch Robert M. Wald. generalrelativity. Founded College. Theoretical physics, general relativity. http://physics.uchicago.edu/t_rel.html

Research Classes Events People ... Physics Home ON THIS PAGE: Sean M. Carroll 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. Sean M. Carroll See Prof. Carroll's entry under Theoretical Astrophysics and Cosmology , or his home page 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.

92. General Relativity Notes By Kristen Wecht Detailed steps on how to Linearize Einstein's field equations of general relativity. http://www.lehigh.edu/~kdw5/project/

General Relativity Tutorials Designed by a Graduate Student for Graduate Students by Kristen Wecht I designed the following general relativity tutorials for beginning graduate students in general relativity. My goal here is to fill in the missing steps between the equations in popular text books on the subject. How to Linearize Einstein's Field Equations (PDF format) How to Construct a Coordinate System That Simplifies the Linearized Field Equations (Work in progress) How to Make Physical Predictions Using the Simplified Linearized Field Equations (Work in progress) Questions or comments? email: Kristen Wecht

93. General Theory Of Relativity In its original form, Einstein's general relativity has been verified numeroustimes in the past 60 years, especially during solareclipse expeditions when http://www.humboldt1.com/~gralsto/einstein/relativ.html

General Theory of Relativity After 1905, Einstein continued working in all three of his works in the 1905 papers Back to Scientific Works Home

94. A Short Course On General Relativity A graduate level course which includes weak field theory, gravitational waves, radiation damping, cosmology, the Friedmann and Lemaitre dusts, singularities, black holes, the Schwarzschild metric and Kruskal's extension of it. This is a single postscript document. http://www.ucolick.org/~burke/class/grclass.ps

95. General Relativity -- From Eric Weisstein's World Of Physics general relativity, References. Adler, R.; Bazin, M.; and Schiffer, M. Introductionto general relativity, 2nd ed. New York McGrawHill, 1975. 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 References 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.

96. Einstein's Theory Of Relativity Website for an online relativity class. Covers special relativity in depth and general relativity at a more qualitative level. Contains tutorial material, references, and links. http://www.drphysics.com/relativity.html

Theory of Relativity What are black holes? What does E=mc mean? How did the Universe begin? How will it end? How is the twin paradox resolved? Learn about Einstein's Theory of Relativity online and find the answers to these questions about the fundamental nature of matter and energy in the Universe. To find out more about the class, go to the Syllabus For a list of suggested readings, click here: Readings Worried about math? Fear not, and click here: Math Register for the class at LearnOnline Rated for content by Internet Content Rating Association Made with 100% recycled materials. No electrons were destroyed to make this website DrPhysics Home Syllabus Readings Math ... Physics Links E-mail the instructor at info@drphysics.com (Hubble Deep Field graphic courtesy of NASA , 1996). For more information about this image, click here

97. Dr. Odenwald's ASK THE ASTRONOMER Page: Relativity FAQs Special general relativity Questions and Answers. The following is a reproductionof the Special and general relativity section of his work. http://einstein.stanford.edu/gen_int/relativity/qanda.html

This information was graciously provided by the NASA-sponsored "Ask the Space Scientist" web page and its author, Dr. Sten Odenwald. The following is a reproduction of the "Special and General Relativity" section of his work. Please visit the site directly How do astronomers tell the difference between the different kinds of redshifts? Could an astronaut use a wrist watch to measure relativistic time dilation? What is it about quantum mechanics that is incompatible with general relativity? ... RETURN to the Question and Answer Index.

98. Reflections On Relativity Comprehensive presentation of the special and general theories of relativity. http://www.mathpages.com/rr/rrtoc.htm

Reflections on Relativity Contents Preface 1. First Principles Experience and Spacetime Systems of Reference Inertia and Relativity The Dilemma of Light ... Null Coordinates 2. A Complex of Phenomena The Spacetime Interval Force Laws and Maxwell's Equations The Inertia of Energy Doppler Shift for Sound and Light ... Thomas Precession 3. Several Valuable Suggestions Postulates and Principles Natural and Violent Motions De Mora Luminis Stationary Paths ... Menelaus and Ceva 4. Weighty Arguments Immovable Spacetime Inertial and Gravitational Separations Free-Fall Equations Force, Curvature, and Uncertainty ... The Breakdown of Simultaneity 5. Extending the Principle Absorbing Acceleration Tensors, Contravariant and Covariant Curvature, Intrinsic and Extrinsic Relatively Straight ... The Field Equations 6. Ist Das Wirklich So? An Exact Solution Anomalous Precession Bending Light Radial Paths in a Spherically Symmetrical Field ... Sources in Motion 7. Cosmology Is the Universe Closed? The Formation and Growth of Black Holes Falling Into and Hovering Near A Black Hole Curled-Up Dimensions ... Global Interpretations of Local Experience 8. The Secret Confidence of Nature Kepler, Napier, and the Third Law

99. SIGRAV The Italian Society of general relativity and Gravitation Via CarloAlberto 10, 10100 TURIN, ITALY. The SIGRAV Executive Board. The Category Science Physics relativity Research Groups http://www.sigrav.unige.it/

Write to our Secretary Scientific Internet sites: McCallum Archive NCSA Relativity Center Grav. Phys. PittsburghRelativity ... ICRA The Italian Society of General Relativity and Gravitation Via Carlo Alberto 10 , 10100 TURIN, ITALY The SIGRAV Executive Board The SIGRAV was founded in 1990 to contribute to the development of the researches on General Relativity and Gravitational Physics, including their mathematical, theoretical, experimental topics and their applications. T he SIGRAV Conferences. The SIGRAV Graduate Schools in contemporary Relativity and Gravitational Physics. The VIRGO-SIGRAV School on Gravitational Waves. ... SIGRAV Activities and info. What's NEW? International call for papers! here details. SIGRAV 2002 Conference The poster SIGRAV 2003 Schools ... 2002 SIGRAV Prizes !

100. Space, Time, And Cosmology Website for an online relativity class. Covers special relativity in depth and general relativity at a more qualitative level. Contains tutorial material, references, and links. http://members.aol.com/drphysics/

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