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General Relativity and Einstein's Equations

Yvonne Choquet-Bruhat

in General Relativity and the Einstein Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199230723
eISBN:
9780191710872
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230723.003.0003
Subject:
Mathematics, Applied Mathematics

This chapter begins with a discussion of Newton's gravity law. It then covers general relativity, observations and experiments, Einstein's equations, field sources, Lagrangians, fluid sources, ... More


Linearized theory and gravitational waves

Ta-Pei Cheng

in Relativity, Gravitation and Cosmology: A Basic Introduction

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199573639
eISBN:
9780191722448
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573639.003.0015
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

In the weak-field limit Einstein's equation can be linearized and it takes on form of the familiar wave equation. Gravitational waves may be viewed as ripples of curvature propagating in a background ... More


The geometric approach to GWs

Michele Maggiore

in Gravitational Waves: Volume 1: Theory and Experiments

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198570745
eISBN:
9780191717666
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570745.003.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses how gravitational waves emerge from general relativity, and what their properties are. The most straightforward approach is ‘linearized theory’, where the Einstein equations ... More


GRAVITATIONAL WAVE EXTRACTION

Miguel Alcubierre

in Introduction to 3+1 Numerical Relativity

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199205677
eISBN:
9780191709371
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205677.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Gravitational waves are one of the most important physical phenomena associated with the presence of strong and dynamic gravitational fields, and as such they are of great interest in numerical ... More


Progressive Waves

Yvonne Choquet-Bruhat

in General Relativity and the Einstein Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199230723
eISBN:
9780191710872
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230723.003.0011
Subject:
Mathematics, Applied Mathematics

This chapter draws on the treatment of progressive waves for non-linear equations used in Sections III.12 and III.13 to construct weak gravitational and electromagnetic waves on a given electrovac ... More


Black Holes and All That Jazz

Valeri P. Frolov and Andrei Zelnikov

in Introduction to Black Hole Physics

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199692293
eISBN:
9780191731860
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199692293.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This Chapter contains a review of many important aspects of modern black hole theory and its applications. It begins with a general definition of a (not‐necessary stationary) black hole and ... More


Introduction to 3+1 Numerical Relativity

Miguel Alcubierre

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199205677
eISBN:
9780191709371
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205677.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book introduces the modern field of 3+1 numerical relativity. It has been written in a way as to be as self-contained as possible, and assumes a basic knowledge of special relativity. Starting ... More


Einstein Equations

Valeri P. Frolov and Andrei Zelnikov

in Introduction to Black Hole Physics

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199692293
eISBN:
9780191731860
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199692293.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

In this Chapter we ‘derive’ the Einstein equations, study their weak field approximation, and briefly discuss gravitational waves and their generation. We finish the Chapter by remarks on the higher ... More


Gravitational physics of few‐body systems

H. Asada, T. Futamase, and P. A. Hogan

in Equations of Motion in General Relativity

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199584109
eISBN:
9780191723421
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199584109.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A subject closely related to equations of motion is the gravitational physics of few body systems. First, the chapter reviews choreographic solutions for the N‐body problem in Newton's theory of ... More


Advanced General Relativity: Gravity Waves, Spinning Particles, and Black Holes

Claude Barrabès and Peter A. Hogan

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199680696
eISBN:
9780191760662
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199680696.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This book is aimed at students who have completed a final year undergraduate course on general relativity and supplemented it with additional techniques by individual study or in a taught MSc ... More


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